Final Group Project
Cecilia Dong
2023-03-01
Load packages
library(tidyverse)
library(tidymodels)
library(janitor)
library(skimr)
library(kableExtra)
library(GGally)
library(vip)
library(fastshap)
library(MASS)
library(ISLR)
library(tree)
library(ggplot2)
library(dplyr)
library(lubridate)
library(imputeTS)
library(forecast)
library(urca)
library(pracma)
library(astsa)
library(fpp2)
library(imputeMissings)Load data with read_csv()
turbine1 <- read_csv("/Users/ceciliadong/Desktop/Forcasting/Final Group Project/Turbine_Data.csv") %>%
clean_names()
#data transformation
turbine1$date <- as.Date(turbine1$date)
head(turbine1) ## # A tibble: 6 × 8
## year month day date active_power ambient_temperature wind_d…¹ wind_…²
## <dbl> <dbl> <dbl> <date> <dbl> <dbl> <dbl> <dbl>
## 1 2017 12 31 2017-12-31 NA NA NA NA
## 2 2017 12 31 2017-12-31 NA NA NA NA
## 3 2017 12 31 2017-12-31 NA NA NA NA
## 4 2017 12 31 2017-12-31 NA NA NA NA
## 5 2017 12 31 2017-12-31 NA NA NA NA
## 6 2017 12 31 2017-12-31 NA NA NA NA
## # … with abbreviated variable names ¹wind_direction, ²wind_speedunique(turbine1$year)## [1] 2017 2018 2019 2020#since we need to provide daily forecast for 2020, we can merely select the data in 2019 and 2020 to do forecast
turbine <- turbine1 %>%
filter(year == 2020 | year == 2019 | year == 2018)
head(turbine)## # A tibble: 6 × 8
## year month day date active_power ambient_temperature wind_d…¹ wind_…²
## <dbl> <dbl> <dbl> <date> <dbl> <dbl> <dbl> <dbl>
## 1 2018 1 1 2018-01-01 -5.36 23.1 8 2.28
## 2 2018 1 1 2018-01-01 -5.82 23.0 300. 2.34
## 3 2018 1 1 2018-01-01 -5.28 22.9 340 2.46
## 4 2018 1 1 2018-01-01 -4.65 23.0 345 2.03
## 5 2018 1 1 2018-01-01 -4.68 22.9 345 1.83
## 6 2018 1 1 2018-01-01 -4.76 22.9 345 1.65
## # … with abbreviated variable names ¹wind_direction, ²wind_speedtail(turbine)## # A tibble: 6 × 8
## year month day date active_power ambient_temperature wind_d…¹ wind_…²
## <dbl> <dbl> <dbl> <date> <dbl> <dbl> <dbl> <dbl>
## 1 2020 3 30 2020-03-30 90.3 27.6 178 3.61
## 2 2020 3 30 2020-03-30 70.0 27.5 178 3.53
## 3 2020 3 30 2020-03-30 40.8 27.6 178 3.26
## 4 2020 3 30 2020-03-30 20.8 27.6 178 3.33
## 5 2020 3 30 2020-03-30 62.1 27.8 190 3.28
## 6 2020 3 30 2020-03-30 68.7 27.9 203 3.48
## # … with abbreviated variable names ¹wind_direction, ²wind_speedLooking at Data quaility
skim(turbine)| Name | turbine |
| Number of rows | 118080 |
| Number of columns | 8 |
| _______________________ | |
| Column type frequency: | |
| Date | 1 |
| numeric | 7 |
| ________________________ | |
| Group variables | None |
Variable type: Date
| skim_variable | n_missing | complete_rate | min | max | median | n_unique |
|---|---|---|---|---|---|---|
| date | 0 | 1 | 2018-01-01 | 2020-03-30 | 2019-02-14 | 820 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| year | 0 | 1.00 | 2018.66 | 0.67 | 2018.00 | 2018.00 | 2019.00 | 2019.00 | 2020.00 | ▇▁▇▁▂ |
| month | 0 | 1.00 | 6.03 | 3.56 | 1.00 | 3.00 | 6.00 | 9.00 | 12.00 | ▇▃▃▃▆ |
| day | 0 | 1.00 | 15.70 | 8.78 | 1.00 | 8.00 | 16.00 | 23.00 | 31.00 | ▇▇▇▇▆ |
| active_power | 23330 | 0.80 | 619.11 | 611.28 | -38.52 | 79.64 | 402.65 | 1074.59 | 1779.03 | ▇▃▂▁▃ |
| ambient_temperature | 24263 | 0.79 | 28.77 | 4.37 | 0.00 | 25.63 | 28.34 | 31.66 | 42.41 | ▁▁▃▇▂ |
| wind_direction | 45802 | 0.61 | 196.29 | 88.30 | 0.00 | 145.00 | 182.00 | 271.00 | 357.00 | ▁▃▇▃▅ |
| wind_speed | 23485 | 0.80 | 5.88 | 2.62 | 0.00 | 3.82 | 5.56 | 7.51 | 22.97 | ▅▇▂▁▁ |
#missing data in active_power, ambient_temperature, wind_direction, wind_speedAccumulate Using a daily index and plot the tine series
turbine_clean <- turbine %>%
na_interpolation()
day_turbine1 <- turbine_clean %>%
group_by(year, month, day) %>%
summarize(active_power = sum(active_power),ambient_temperature = mean(ambient_temperature),
wind_direction=mean(wind_direction), wind_speed=mean(wind_speed))
head(day_turbine1)## # A tibble: 6 × 7
## # Groups: year, month [1]
## year month day active_power ambient_temperature wind_direction wind_speed
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2018 1 1 27571. 26.5 282. 3.88
## 2 2018 1 2 48502. 25.6 273. 4.67
## 3 2018 1 3 45905. 25.5 276. 4.53
## 4 2018 1 4 51965. 24.9 285. 5.06
## 5 2018 1 5 34609. 24.6 281. 4.42
## 6 2018 1 6 19548. 22.6 312. 3.81#drop everything but the series
day_turbine <- subset(day_turbine1, select = -c(year,month,day, ambient_temperature, wind_direction, wind_speed))
head(day_turbine)## # A tibble: 6 × 1
## active_power
## <dbl>
## 1 27571.
## 2 48502.
## 3 45905.
## 4 51965.
## 5 34609.
## 6 19548.## Create a daily Date object - helps my work on dates
inds <- seq(as.Date("2020-01-01"), as.Date("2020-03-30"), by = "day")
as.numeric(format(inds[1], "%j"))## [1] 1## Create a time series object
turbine_ts <- ts(day_turbine, start=c(2018,1), frequency = 365)
plot(turbine_ts)
turbine_tsi <- na_interpolation(turbine_ts)
print(turbine_tsi)## Time Series:
## Start = c(2018, 1)
## End = c(2020, 90)
## Frequency = 365
## active_power
## [1,] 27570.7490
## [2,] 48501.8066
## [3,] 45904.8192
## [4,] 51965.3897
## [5,] 34608.7212
## [6,] 19547.6142
## [7,] 51213.1585
## [8,] 109448.1129
## [9,] 73036.1857
## [10,] 63902.4295
## [11,] 61334.3685
## [12,] 22953.0853
## [13,] 51947.0029
## [14,] 78659.0128
## [15,] 28028.4875
## [16,] 57517.5491
## [17,] 58322.8032
## [18,] 62372.4582
## [19,] 52478.7977
## [20,] 32712.2594
## [21,] 68070.9847
## [22,] 54241.9801
## [23,] 575.8896
## [24,] 19003.0921
## [25,] 35369.2910
## [26,] 27638.6489
## [27,] 37203.0604
## [28,] 89179.6072
## [29,] 68457.4715
## [30,] 64474.1900
## [31,] 60490.9085
## [32,] 56507.6271
## [33,] 52524.3456
## [34,] 48541.0641
## [35,] 44557.7826
## [36,] 82866.0597
## [37,] 27091.2670
## [38,] 323.2630
## [39,] -806.0467
## [40,] 24529.5492
## [41,] 74559.3573
## [42,] 145699.8866
## [43,] 107534.0413
## [44,] 102250.9333
## [45,] 110567.3547
## [46,] 68428.7233
## [47,] 24990.6226
## [48,] 29073.9695
## [49,] 69059.6228
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## [51,] 65055.2261
## [52,] 72437.6783
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## [72,] 53503.7587
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## [817,] 103492.1290
## [818,] 95972.5666
## [819,] 114258.5268
## [820,] 105566.5782plot(turbine_tsi)
Test original series for stationary
Box.test(turbine_tsi, lag=8, fitdf=0, type="Lj")##
## Box-Ljung test
##
## data: turbine_tsi
## X-squared = 3437, df = 8, p-value < 2.2e-16#Ho: white noise
#Ha: not white noise
#p value < 0.05, reject Ho, the original turbine_ts series is not white noise, so we need to build model for itPlot ACF and PACF for turbine and test for stationary
plot(turbine_tsi)
ggAcf(turbine_tsi)
#ACF quickly decays to 0
ggPacf(turbine_tsi)
#lag 1 is positive in PACF, suggesting autoregression
#test for stationary
turbine_df <- ur.df(turbine_tsi, type = "drift")
summary(turbine_df)##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression drift
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -159375 -19053 -292 17268 123299
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9222.39368 1821.86442 5.062 5.13e-07 ***
## z.lag.1 -0.10080 0.01597 -6.312 4.52e-10 ***
## z.diff.lag -0.03374 0.03499 -0.964 0.335
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31600 on 815 degrees of freedom
## Multiple R-squared: 0.05333, Adjusted R-squared: 0.051
## F-statistic: 22.96 on 2 and 815 DF, p-value: 2.002e-10
##
##
## Value of test-statistic is: -6.312 19.9232
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1 6.43 4.59 3.78#H0:nonstationary and needs a 1st difference
#Ha: Stationary (does not need a first diff)
#p value of z.lag.1 is less than 0.05, reject Ho, series turbine_tsi is stationary, d = 0Fit Simple ESM Model
turbine_esm <- ses(turbine_tsi, h=5)
summary(turbine_esm)##
## Forecast method: Simple exponential smoothing
##
## Model Information:
## Simple exponential smoothing
##
## Call:
## ses(y = turbine_tsi, h = 5)
##
## Smoothing parameters:
## alpha = 0.885
##
## Initial states:
## l = 30061.9863
##
## sigma: 32271.66
##
## AIC AICc BIC
## 22532.02 22532.05 22546.14
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 105.1025 32232.28 23325.22 -Inf Inf 0.5365042 0.01590287
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2020.2466 106333.8 64975.97 147691.6 43082.472 169585.1
## 2020.2493 106333.8 51105.97 161561.6 21870.147 190797.4
## 2020.2521 106333.8 40078.57 172589.0 5005.193 207662.3
## 2020.2548 106333.8 30641.02 182026.5 -9428.303 222095.8
## 2020.2575 106333.8 22256.22 190411.3 -22251.744 234919.3# RMSE = 32232.28, MAE = 23325.22, forecast errors are not decent
forecast(turbine_esm)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2020.2466 106333.8 64975.97 147691.6 43082.472 169585.1
## 2020.2493 106333.8 51105.97 161561.6 21870.147 190797.4
## 2020.2521 106333.8 40078.57 172589.0 5005.193 207662.3
## 2020.2548 106333.8 30641.02 182026.5 -9428.303 222095.8
## 2020.2575 106333.8 22256.22 190411.3 -22251.744 234919.3turbine_esm %>% forecast() %>% autoplot()
Try auto.arima
fit_auto <- auto.arima(turbine_tsi, xreg = as.matrix(day_turbine1[, 5:7]))
summary(fit_auto)## Series: turbine_tsi
## Regression with ARIMA(1,0,1) errors
##
## Coefficients:
## ar1 ma1 intercept ambient_temperature wind_direction
## 0.7001 0.2075 -60012.68 -432.6182 -18.7551
## s.e. 0.0346 0.0465 11867.09 373.7633 16.3386
## wind_speed
## 27984.5680
## s.e. 576.9068
##
## sigma^2 = 259403820: log likelihood = -9104.31
## AIC=18222.62 AICc=18222.76 BIC=18255.59
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 3.655038 16046.99 10326.17 -Inf Inf 0.2375126 -0.001151008checkresiduals(fit_auto)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(1,0,1) errors
## Q* = 251.67, df = 162, p-value = 8.019e-06
##
## Model df: 2. Total lags used: 164#RMSE = 16046.99, MAE = 10326.17, better than using simple ESM model
fit1_auto <- sarima(turbine_tsi, 1, 0, 1,xreg = as.matrix(day_turbine1[, 5:7]))## initial value 10.126967
## iter 2 value 9.932420
## iter 3 value 9.707907
## iter 4 value 9.701572
## iter 5 value 9.698732
## iter 6 value 9.687617
## iter 7 value 9.685632
## iter 8 value 9.684290
## iter 9 value 9.684031
## iter 10 value 9.683910
## iter 11 value 9.683904
## iter 12 value 9.683897
## iter 13 value 9.683887
## iter 14 value 9.683879
## iter 15 value 9.683878
## iter 16 value 9.683878
## iter 17 value 9.683877
## iter 18 value 9.683877
## iter 19 value 9.683876
## iter 20 value 9.683876
## iter 20 value 9.683876
## iter 20 value 9.683876
## final value 9.683876
## converged
## initial value 9.683880
## iter 2 value 9.683879
## iter 2 value 9.683879
## iter 2 value 9.683879
## final value 9.683879
## converged
fit1_auto## $fit
##
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D,
## Q), period = S), xreg = xreg, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc,
## REPORT = 1, reltol = tol))
##
## Coefficients:
## ar1 ma1 intercept ambient_temperature wind_direction
## 0.7001 0.2075 -60012.68 -432.6182 -18.7551
## s.e. 0.0346 0.0465 11867.09 373.7633 16.3386
## wind_speed
## 27984.5680
## s.e. 576.9068
##
## sigma^2 estimated as 257505743: log likelihood = -9104.31, aic = 18222.62
##
## $degrees_of_freedom
## [1] 814
##
## $ttable
## Estimate SE t.value p.value
## ar1 0.7001 0.0346 20.2122 0.0000
## ma1 0.2075 0.0465 4.4582 0.0000
## intercept -60012.6769 11867.0865 -5.0571 0.0000
## ambient_temperature -432.6182 373.7633 -1.1575 0.2474
## wind_direction -18.7551 16.3386 -1.1479 0.2513
## wind_speed 27984.5680 576.9068 48.5080 0.0000
##
## $AIC
## [1] 22.22271
##
## $AICc
## [1] 22.22283
##
## $BIC
## [1] 22.26291#Residuals are not white noise; temperature and direction are not significant
#Not all the ACF are within the error bond, is not white noise
accuracy(fit_auto)## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 3.655038 16046.99 10326.17 -Inf Inf 0.2375126 -0.001151008#fit_auto %>% forecast() %>% autoplot()
##create forecast and actual data line together, create overlap plot
#red line deviates from the balck peaks and bottoms
ts.plot(turbine_tsi, fitted(fit_auto), gpars=list(col=c("black","red")))
#seems resonableTry intervention and iteratly select the best model
fit_AR1 <- Arima(turbine_tsi, xreg = day_turbine1$wind_speed, order = c(1,0,1))
summary(fit_AR1)## Series: turbine_tsi
## Regression with ARIMA(1,0,1) errors
##
## Coefficients:
## ar1 ma1 intercept xreg
## 0.7011 0.2035 -75857.82 27932.79
## s.e. 0.0341 0.0463 4098.91 574.53
##
## sigma^2 = 259637818: log likelihood = -9105.68
## AIC=18221.37 AICc=18221.44 BIC=18244.92
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 7.072441 16073.93 10296.59 -Inf Inf 0.2368323 -0.0006827484checkresiduals(fit_AR1)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(1,0,1) errors
## Q* = 253.13, df = 162, p-value = 6.078e-06
##
## Model df: 2. Total lags used: 164#RMSE = 16073.93, MAE = 10296.59
fit1_AR <- sarima(turbine_tsi, 1, 0, 1,xreg = day_turbine1$wind_speed)## initial value 10.135842
## iter 2 value 9.942492
## iter 3 value 9.706225
## iter 4 value 9.700462
## iter 5 value 9.697852
## iter 6 value 9.691525
## iter 7 value 9.688465
## iter 8 value 9.686646
## iter 9 value 9.685844
## iter 10 value 9.685614
## iter 11 value 9.685577
## iter 12 value 9.685551
## iter 13 value 9.685548
## iter 14 value 9.685547
## iter 14 value 9.685547
## iter 14 value 9.685547
## final value 9.685547
## converged
## initial value 9.685557
## iter 2 value 9.685556
## iter 3 value 9.685556
## iter 4 value 9.685555
## iter 5 value 9.685555
## iter 5 value 9.685555
## iter 5 value 9.685555
## final value 9.685555
## converged
fit1_AR## $fit
##
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D,
## Q), period = S), xreg = xreg, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc,
## REPORT = 1, reltol = tol))
##
## Coefficients:
## ar1 ma1 intercept xreg
## 0.7011 0.2035 -75857.82 27932.79
## s.e. 0.0341 0.0463 4098.91 574.53
##
## sigma^2 estimated as 258371292: log likelihood = -9105.68, aic = 18221.37
##
## $degrees_of_freedom
## [1] 816
##
## $ttable
## Estimate SE t.value p.value
## ar1 0.7011 0.0341 20.5423 0
## ma1 0.2035 0.0463 4.3908 0
## intercept -75857.8216 4098.9101 -18.5068 0
## xreg 27932.7931 574.5300 48.6185 0
##
## $AIC
## [1] 22.22118
##
## $AICc
## [1] 22.22124
##
## $BIC
## [1] 22.2499#All the terms are significant, residuals are not white noise; relatively high forecast error
fit_AR2 <- Arima(turbine_tsi, xreg = day_turbine1$wind_speed, order = c(1,1,1))
summary(fit_AR2)## Series: turbine_tsi
## Regression with ARIMA(1,1,1) errors
##
## Coefficients:
## ar1 ma1 xreg
## -0.6622 0.7374 26709.0723
## s.e. 0.1150 0.1022 577.9466
##
## sigma^2 = 293680665: log likelihood = -9145.05
## AIC=18298.1 AICc=18298.15 BIC=18316.93
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 25.6462 17095.26 11094.76 NaN Inf 0.2551909 -0.04550076checkresiduals(fit_AR2)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(1,1,1) errors
## Q* = 263.36, df = 162, p-value = 8.19e-07
##
## Model df: 2. Total lags used: 164#RMSE = 17095.26, MAE = 11094.76
fit2_AR <- sarima(turbine_tsi, 1, 1, 1,xreg = day_turbine1$wind_speed)## initial value 9.752700
## iter 2 value 9.752627
## iter 3 value 9.752545
## iter 4 value 9.752541
## iter 5 value 9.752315
## iter 6 value 9.751967
## iter 7 value 9.751760
## iter 8 value 9.751429
## iter 9 value 9.750927
## iter 10 value 9.749881
## iter 11 value 9.749806
## iter 12 value 9.749589
## iter 13 value 9.749237
## iter 14 value 9.748830
## iter 15 value 9.748505
## iter 16 value 9.748326
## iter 17 value 9.748106
## iter 18 value 9.747927
## iter 19 value 9.747861
## iter 20 value 9.747846
## iter 21 value 9.747832
## iter 22 value 9.747828
## iter 23 value 9.747821
## iter 24 value 9.747799
## iter 25 value 9.747787
## iter 26 value 9.747783
## iter 27 value 9.747782
## iter 28 value 9.747780
## iter 29 value 9.747779
## iter 30 value 9.747779
## iter 31 value 9.747778
## iter 32 value 9.747778
## iter 32 value 9.747778
## iter 32 value 9.747778
## final value 9.747778
## converged
## initial value 9.747180
## iter 1 value 9.747180
## final value 9.747180
## converged
fit2_AR## $fit
##
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D,
## Q), period = S), xreg = xreg, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc,
## REPORT = 1, reltol = tol))
##
## Coefficients:
## ar1 ma1 xreg
## -0.6622 0.7374 26709.0723
## s.e. 0.1150 0.1022 577.9466
##
## sigma^2 estimated as 292604904: log likelihood = -9145.05, aic = 18298.1
##
## $degrees_of_freedom
## [1] 816
##
## $ttable
## Estimate SE t.value p.value
## ar1 -0.6622 0.1150 -5.7574 0
## ma1 0.7374 0.1022 7.2192 0
## xreg 26709.0723 577.9466 46.2137 0
##
## $AIC
## [1] 22.34201
##
## $AICc
## [1] 22.34204
##
## $BIC
## [1] 22.365#Residuals are not white noise; high forecast error
fit_AR4 <- Arima(turbine_tsi, xreg = day_turbine1$wind_speed, order = c(3,1,1))
summary(fit_AR4)## Series: turbine_tsi
## Regression with ARIMA(3,1,1) errors
##
## Coefficients:
## ar1 ar2 ar3 ma1 xreg
## 0.8594 -0.1616 -0.0171 -0.9605 27317.2767
## s.e. 0.0373 0.0459 0.0363 0.0132 588.7666
##
## sigma^2 = 259510578: log likelihood = -9094
## AIC=18199.99 AICc=18200.1 BIC=18228.24
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 94.84751 16050.29 10314.68 -Inf Inf 0.2372484 -0.00122635checkresiduals(fit_AR4)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(3,1,1) errors
## Q* = 229.39, df = 160, p-value = 0.0002662
##
## Model df: 4. Total lags used: 164#RMSE = 16050.29, MAE = 10314.68
fit4_AR <- sarima(turbine_tsi, 3, 1, 1,xreg = day_turbine1$wind_speed)## initial value 9.753782
## iter 2 value 9.740178
## iter 3 value 9.739763
## iter 4 value 9.739105
## iter 5 value 9.738675
## iter 6 value 9.734370
## iter 7 value 9.730971
## iter 8 value 9.717202
## iter 9 value 9.715762
## iter 10 value 9.697615
## iter 11 value 9.695909
## iter 12 value 9.694091
## iter 13 value 9.691296
## iter 14 value 9.688264
## iter 15 value 9.687930
## iter 16 value 9.687826
## iter 17 value 9.687655
## iter 18 value 9.687627
## iter 19 value 9.687611
## iter 20 value 9.687606
## iter 21 value 9.687605
## iter 21 value 9.687605
## iter 21 value 9.687605
## final value 9.687605
## converged
## initial value 9.684970
## iter 2 value 9.684938
## iter 3 value 9.684872
## iter 4 value 9.684854
## iter 5 value 9.684849
## iter 6 value 9.684846
## iter 7 value 9.684843
## iter 8 value 9.684843
## iter 8 value 9.684842
## iter 8 value 9.684842
## final value 9.684842
## converged
fit4_AR## $fit
##
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D,
## Q), period = S), xreg = xreg, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc,
## REPORT = 1, reltol = tol))
##
## Coefficients:
## ar1 ar2 ar3 ma1 xreg
## 0.8594 -0.1616 -0.0171 -0.9605 27317.2767
## s.e. 0.0373 0.0459 0.0363 0.0132 588.7666
##
## sigma^2 estimated as 257926257: log likelihood = -9094, aic = 18199.99
##
## $degrees_of_freedom
## [1] 814
##
## $ttable
## Estimate SE t.value p.value
## ar1 0.8594 0.0373 23.0210 0.0000
## ar2 -0.1616 0.0459 -3.5247 0.0004
## ar3 -0.0171 0.0363 -0.4704 0.6382
## ma1 -0.9605 0.0132 -72.9282 0.0000
## xreg 27317.2767 588.7666 46.3975 0.0000
##
## $AIC
## [1] 22.22221
##
## $AICc
## [1] 22.2223
##
## $BIC
## [1] 22.25671#Residuals are not white noise; ar3 is not significant
fit_AR5 <- Arima(turbine_tsi, xreg = day_turbine1$wind_speed, order = c(2,1,2))
summary(fit_AR5)## Series: turbine_tsi
## Regression with ARIMA(2,1,2) errors
##
## Coefficients:
## ar1 ar2 ma1 ma2 xreg
## 0.3350 0.2391 -0.4383 -0.5143 27315.5935
## s.e. 0.2129 0.1734 0.2009 0.1979 589.4629
##
## sigma^2 = 259801848: log likelihood = -9094.47
## AIC=18200.93 AICc=18201.04 BIC=18229.18
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 95.62227 16059.29 10298.89 -Inf Inf 0.2368851 0.01207915checkresiduals(fit_AR5)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(2,1,2) errors
## Q* = 218.32, df = 160, p-value = 0.001501
##
## Model df: 4. Total lags used: 164#RMSE = 16059.29, MAE = 10298.89
fit5_AR <- sarima(turbine_tsi, 2, 1, 2,xreg = day_turbine1$wind_speed)## initial value 9.753309
## iter 2 value 9.744518
## iter 3 value 9.739097
## iter 4 value 9.737658
## iter 5 value 9.732995
## iter 6 value 9.730230
## iter 7 value 9.726200
## iter 8 value 9.722472
## iter 9 value 9.704696
## iter 10 value 9.697101
## iter 11 value 9.692904
## iter 12 value 9.692020
## iter 13 value 9.688949
## iter 14 value 9.686856
## iter 15 value 9.686612
## iter 16 value 9.686320
## iter 17 value 9.686184
## iter 18 value 9.686072
## iter 19 value 9.686016
## iter 20 value 9.685989
## iter 21 value 9.685988
## iter 22 value 9.685983
## iter 23 value 9.685976
## iter 24 value 9.685940
## iter 25 value 9.685927
## iter 26 value 9.685918
## iter 27 value 9.685910
## iter 28 value 9.685898
## iter 29 value 9.685890
## iter 30 value 9.685888
## iter 30 value 9.685888
## iter 30 value 9.685888
## final value 9.685888
## converged
## initial value 9.685431
## iter 2 value 9.685422
## iter 3 value 9.685418
## iter 4 value 9.685417
## iter 5 value 9.685416
## iter 6 value 9.685416
## iter 7 value 9.685415
## iter 7 value 9.685415
## iter 7 value 9.685415
## final value 9.685415
## converged
fit5_AR## $fit
##
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D,
## Q), period = S), xreg = xreg, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc,
## REPORT = 1, reltol = tol))
##
## Coefficients:
## ar1 ar2 ma1 ma2 xreg
## 0.3350 0.2391 -0.4383 -0.5143 27315.5935
## s.e. 0.2129 0.1734 0.2009 0.1979 589.4629
##
## sigma^2 estimated as 258215749: log likelihood = -9094.47, aic = 18200.93
##
## $degrees_of_freedom
## [1] 814
##
## $ttable
## Estimate SE t.value p.value
## ar1 0.3350 0.2129 1.5731 0.1161
## ar2 0.2391 0.1734 1.3785 0.1684
## ma1 -0.4383 0.2009 -2.1819 0.0294
## ma2 -0.5143 0.1979 -2.5992 0.0095
## xreg 27315.5935 589.4629 46.3398 0.0000
##
## $AIC
## [1] 22.22336
##
## $AICc
## [1] 22.22345
##
## $BIC
## [1] 22.25785#Residuals are not white noise; ar1 and ar2 are not significant
fit_AR3 <- Arima(turbine_tsi, xreg = day_turbine1$wind_speed, order = c(2,1,1))
summary(fit_AR3)## Series: turbine_tsi
## Regression with ARIMA(2,1,1) errors
##
## Coefficients:
## ar1 ar2 ma1 xreg
## 0.8637 -0.1753 -0.9621 27316.7580
## s.e. 0.0361 0.0355 0.0125 589.2288
##
## sigma^2 = 259262026: log likelihood = -9094.11
## AIC=18198.21 AICc=18198.29 BIC=18221.75
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 95.09323 16052.45 10319.95 -Inf Inf 0.2373695 -0.002897159checkresiduals(fit_AR3)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(2,1,1) errors
## Q* = 229.75, df = 161, p-value = 0.0003047
##
## Model df: 3. Total lags used: 164#RMSE = 16052.45， MAE = 10319.95, final model
fit3_AR <- sarima(turbine_tsi, 2, 1, 1,xreg = day_turbine1$wind_speed)## initial value 9.753309
## iter 2 value 9.743147
## iter 3 value 9.743025
## iter 4 value 9.742825
## iter 5 value 9.742674
## iter 6 value 9.741374
## iter 7 value 9.739876
## iter 8 value 9.738678
## iter 9 value 9.736465
## iter 10 value 9.731963
## iter 11 value 9.718832
## iter 12 value 9.697546
## iter 13 value 9.696918
## iter 14 value 9.695169
## iter 15 value 9.685697
## iter 16 value 9.684245
## iter 16 value 9.684245
## iter 17 value 9.683087
## iter 17 value 9.683087
## iter 18 value 9.683086
## iter 18 value 9.683086
## iter 18 value 9.683086
## final value 9.683086
## converged
## initial value 9.689189
## iter 2 value 9.686989
## iter 3 value 9.686621
## iter 4 value 9.685313
## iter 5 value 9.685113
## iter 6 value 9.685077
## iter 7 value 9.684987
## iter 8 value 9.684978
## iter 9 value 9.684977
## iter 9 value 9.684977
## iter 9 value 9.684977
## final value 9.684977
## converged
fit3_AR## $fit
##
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D,
## Q), period = S), xreg = xreg, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc,
## REPORT = 1, reltol = tol))
##
## Coefficients:
## ar1 ar2 ma1 xreg
## 0.8637 -0.1753 -0.9621 27316.7580
## s.e. 0.0361 0.0355 0.0125 589.2288
##
## sigma^2 estimated as 2.58e+08: log likelihood = -9094.11, aic = 18198.21
##
## $degrees_of_freedom
## [1] 815
##
## $ttable
## Estimate SE t.value p.value
## ar1 0.8637 0.0361 23.8942 0
## ar2 -0.1753 0.0355 -4.9422 0
## ma1 -0.9621 0.0125 -76.8522 0
## xreg 27316.7580 589.2288 46.3602 0
##
## $AIC
## [1] 22.22004
##
## $AICc
## [1] 22.2201
##
## $BIC
## [1] 22.24878#All the terms are significant
day_turbine2 <- day_turbine1 %>%
dplyr::select(ambient_temperature, wind_speed)
day_turbine3 <- subset(day_turbine2, select = -c(year,month))
fit_AR6 <- Arima(turbine_tsi, xreg = as.matrix(day_turbine3), order = c(2,1,1))
summary(fit_AR6)## Series: turbine_tsi
## Regression with ARIMA(2,1,1) errors
##
## Coefficients:
## ar1 ar2 ma1 ambient_temperature wind_speed
## 0.8657 -0.1780 -0.9618 -741.0703 27282.4314
## s.e. 0.0360 0.0355 0.0118 395.0563 584.3959
##
## sigma^2 = 258466379: log likelihood = -9092.34
## AIC=18196.69 AICc=18196.79 BIC=18224.94
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 122.1142 16017.96 10295.71 -Inf Inf 0.2368121 -0.003687783checkresiduals(fit_AR6)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(2,1,1) errors
## Q* = 227.89, df = 161, p-value = 0.0004117
##
## Model df: 3. Total lags used: 164fit_AR7 <- Arima(turbine_tsi, xreg = as.matrix(day_turbine3), order = c(1,0,1))
summary(fit_AR7)## Series: turbine_tsi
## Regression with ARIMA(1,0,1) errors
##
## Coefficients:
## ar1 ma1 intercept ambient_temperature wind_speed
## 0.7049 0.2028 -62753.58 -452.6613 27905.0986
## s.e. 0.0340 0.0461 11644.31 374.5446 574.9022
##
## sigma^2 = 259500585: log likelihood = -9104.97
## AIC=18221.94 AICc=18222.04 BIC=18250.2
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 9.267208 16059.83 10327.9 -Inf Inf 0.2375523 -0.0005434625checkresiduals(fit_AR7)
##
## Ljung-Box test
##
## data: Residuals from Regression with ARIMA(1,0,1) errors
## Q* = 256.31, df = 162, p-value = 3.299e-06
##
## Model df: 2. Total lags used: 164#RMSE: 16059.83 MAE:10327.9
fit8_AR <- sarima(turbine_tsi, 2, 1, 1,xreg = as.matrix(day_turbine3))## initial value 9.751478
## iter 2 value 9.741750
## iter 3 value 9.741607
## iter 4 value 9.741390
## iter 5 value 9.741237
## iter 6 value 9.740038
## iter 7 value 9.737884
## iter 8 value 9.731052
## iter 9 value 9.718287
## iter 10 value 9.707457
## iter 11 value 9.698241
## iter 12 value 9.690002
## iter 13 value 9.687652
## iter 14 value 9.685888
## iter 15 value 9.684702
## iter 16 value 9.684025
## iter 17 value 9.683474
## iter 18 value 9.683401
## iter 19 value 9.683394
## iter 20 value 9.683392
## iter 21 value 9.683392
## iter 22 value 9.683391
## iter 23 value 9.683389
## iter 24 value 9.683388
## iter 25 value 9.683388
## iter 25 value 9.683388
## iter 25 value 9.683388
## final value 9.683388
## converged
## initial value 9.682834
## iter 2 value 9.682827
## iter 3 value 9.682825
## iter 4 value 9.682825
## iter 4 value 9.682825
## iter 4 value 9.682825
## final value 9.682825
## converged
fit8_AR## $fit
##
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D,
## Q), period = S), xreg = xreg, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc,
## REPORT = 1, reltol = tol))
##
## Coefficients:
## ar1 ar2 ma1 ambient_temperature wind_speed
## 0.8657 -0.1780 -0.9618 -741.0703 27282.4314
## s.e. 0.0360 0.0355 0.0118 395.0563 584.3959
##
## sigma^2 estimated as 256888436: log likelihood = -9092.34, aic = 18196.69
##
## $degrees_of_freedom
## [1] 814
##
## $ttable
## Estimate SE t.value p.value
## ar1 0.8657 0.0360 24.0276 0.000
## ar2 -0.1780 0.0355 -5.0221 0.000
## ma1 -0.9618 0.0118 -81.4843 0.000
## ambient_temperature -741.0703 395.0563 -1.8759 0.061
## wind_speed 27282.4314 584.3959 46.6848 0.000
##
## $AIC
## [1] 22.21818
##
## $AICc
## [1] 22.21827
##
## $BIC
## [1] 22.25267#RMSE = 16017.96, MAE = 10295.71, better than auto.arima, all the terms are significant, final model
accuracy(fit_AR3)## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 95.09323 16052.45 10319.95 -Inf Inf 0.2373695 -0.002897159autoplot(forecast(fit_AR3, xreg = day_turbine1$wind_speed))
fit_AR3 %>%
forecast(xreg = day_turbine1$wind_speed, h=5)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2020.2466 45078.3186 24443.2679 65713.37 13519.7319 76636.91
## 2020.2493 62630.4158 34846.9480 90413.88 20139.2686 105121.56
## 2020.2521 56065.4931 25291.5225 86839.46 9000.7665 103130.22
## 2020.2548 69129.7260 37080.6595 101178.79 20114.9085 118144.54
## 2020.2575 50686.7106 18044.8884 83328.53 765.3516 100608.07
## 2020.2603 33479.5874 520.6168 66438.56 -16926.8083 83885.98
## 2020.2630 73782.9851 40624.0776 106941.89 23070.8122 124495.16
## 2020.2658 113424.7101 80119.1099 146730.31 62488.1901 164361.23
## 2020.2685 83082.7729 49656.1979 116509.35 31961.2380 134204.31
## 2020.2712 75992.9393 42458.4278 109527.45 24706.3298 127279.55
## 2020.2740 72230.1099 38594.5200 105865.70 20788.9143 123671.31
## 2020.2767 35418.4035 1685.4592 69151.35 -16171.6828 87008.49
## 2020.2795 60814.5897 26986.3856 94642.79 9078.8162 112550.36
## 2020.2822 76466.7075 42544.4786 110388.94 24587.1353 128346.28
## 2020.2849 46887.6482 12872.1714 80903.12 -5134.5343 98909.83
## 2020.2877 70230.4718 36122.2790 104338.66 18066.4924 122394.45
## 2020.2904 65186.4556 30985.9465 99386.96 12881.2906 117491.62
## 2020.2932 80721.6537 46429.1563 115014.15 28275.8048 133167.50
## 2020.2959 63007.0623 28622.8655 97391.26 10420.9712 115593.15
## 2020.2986 49429.1149 14953.4853 83904.74 -3296.8105 102155.04
## 2020.3014 71319.4266 36752.6184 105886.23 18454.0555 124184.80
## 2020.3041 64439.1014 29781.3610 99096.84 11434.6615 117443.54
## 2020.3068 4177.3855 -30571.0456 38925.82 -48965.7538 57320.52
## 2020.3096 24182.0080 -10656.8758 59020.89 -29099.4668 77463.48
## 2020.3123 42460.4830 7531.3818 77389.58 -10958.9675 95879.93
## 2020.3151 42544.0229 7524.9372 77563.11 -11013.0470 96101.09
## 2020.3178 44225.9781 9117.1387 79334.82 -9468.3582 97920.31
## 2020.3205 101608.9034 66410.5395 136807.27 47777.6511 155440.16
## 2020.3233 93571.3039 58283.6426 128858.97 39603.4831 147539.12
## 2020.3260 87268.3168 51891.5836 122645.05 33164.2723 141372.36
## 2020.3288 80965.3298 45499.7485 116430.91 26725.4038 135205.26
## 2020.3315 74662.3429 39108.1354 110216.55 20286.8749 129037.81
## 2020.3342 68359.3560 32716.7428 104001.97 13848.6831 122870.03
## 2020.3370 62056.3691 26325.5689 97787.17 7410.8258 116701.91
## 2020.3397 55753.3822 19934.6121 91572.15 973.3005 110533.46
## 2020.3425 88489.2753 52582.7508 124395.80 33574.9849 143403.57
## 2020.3452 37800.8287 1806.7637 73794.89 -17247.3433 92849.00
## 2020.3479 7888.7030 -28192.6900 43970.10 -47293.0256 63070.43
## 2020.3507 -5503.1198 -41671.6300 30665.39 -60818.0827 49811.84
## 2020.3534 32225.1627 -4030.2554 68480.58 -23222.7144 87673.04
## 2020.3562 73456.0325 37113.9144 109798.15 17875.5592 129036.51
## 2020.3589 121857.7221 85429.1104 158286.33 66144.9682 177570.48
## 2020.3616 98562.0859 62047.1853 135076.99 42717.3646 154406.81
## 2020.3644 102733.7792 66132.7933 139334.77 46757.4017 158710.16
## 2020.3671 108996.2720 72309.4027 145683.14 52888.5472 165104.00
## 2020.3699 74140.1659 37367.6138 110912.72 17901.4006 130378.93
## 2020.3726 33631.1451 -3226.8907 70489.18 -22738.3562 90000.65
## 2020.3753 34296.6064 -2646.7151 71239.93 -22203.3282 90796.54
## 2020.3781 75540.4970 38512.0861 112568.91 18910.4294 132170.56
## 2020.3808 83496.2924 46382.9873 120609.60 26736.3903 140256.19
## 2020.3836 74627.4401 37429.4344 111825.45 17737.9996 131516.88
## 2020.3863 74834.5157 37552.0019 112117.03 17815.8312 131853.20
## 2020.3890 71174.9160 33808.0851 108541.75 14027.2798 128322.55
## 2020.3918 97407.9956 59957.0376 134858.95 40131.6980 154684.29
## 2020.3945 94208.7212 56673.8246 131743.62 36804.0505 151613.39
## 2020.3973 64571.4871 26952.8392 102190.14 7038.7299 122104.24
## 2020.4000 63029.3241 25327.1109 100731.54 5368.7648 120689.88
## 2020.4027 72563.2000 34777.6063 110348.79 14775.1213 130351.28
## 2020.4055 48919.9541 11051.1635 86788.74 -8995.3633 106835.27
## 2020.4082 72358.0517 34406.2467 110309.86 14315.7746 130400.33
## 2020.4110 78177.4859 40142.8476 116212.12 20008.5263 136346.45
## 2020.4137 83504.8764 45387.5848 121622.17 25209.5094 141800.24
## 2020.4164 85758.3260 47558.5599 123958.09 27336.8253 144179.83
## 2020.4192 690.5116 -37591.5512 38972.57 -57856.8512 59237.87
## 2020.4219 14333.8037 -24030.3795 52697.99 -44339.1513 73006.76
## 2020.4247 27977.0957 -10469.0323 66423.22 -30821.1831 86775.37
## 2020.4274 41620.3877 3092.4891 80148.29 -17302.9483 100543.72
## 2020.4301 55263.6797 16654.1838 93873.18 -3784.4487 114311.81
## 2020.4329 68906.9717 30216.0505 107597.89 9734.3141 128079.63
## 2020.4356 82550.2637 43778.0882 121322.44 23253.3384 141847.19
## 2020.4384 95192.0477 56338.7879 134045.31 35771.1146 154612.98
## 2020.4411 61967.5002 23033.3249 100901.68 2422.8175 121512.18
## 2020.4438 72504.8458 33489.9228 111519.77 12836.6702 132173.02
## 2020.4466 75151.2275 36055.7237 114246.73 15359.8140 134942.64
## 2020.4493 29512.3184 -9663.6006 68688.24 -30402.0794 89426.72
## 2020.4521 59236.8627 19980.6933 98493.03 -800.2676 119273.99
## 2020.4548 28921.2484 -10415.0078 68257.50 -31238.3639 89080.86
## 2020.4575 65525.1151 26108.9350 104941.30 5243.2696 125806.96
## 2020.4603 -6332.2879 -45828.2303 33163.65 -66736.1192 54071.54
## 2020.4630 13722.2848 -25853.2591 53297.83 -46803.2865 74247.86
## 2020.4658 38961.7748 -693.2108 78616.76 -21685.2921 99608.84
## 2020.4685 64201.2648 24466.9963 103935.53 3432.9452 124969.58
## 2020.4712 89440.7548 49627.3614 129254.15 28551.4240 150330.09
## 2020.4740 101837.8034 61945.4419 141730.16 40827.7013 162847.91
## 2020.4767 73546.9211 33575.7476 113518.09 12416.2864 134677.56
## 2020.4795 51163.6684 11113.8379 91213.50 -10087.2617 112414.60
## 2020.4822 56729.7509 16601.4176 96858.08 -4641.2388 118100.74
## 2020.4849 49821.3723 9614.6895 90028.06 -11669.4427 111312.19
## 2020.4877 79247.7288 38962.8489 119532.61 17637.3216 140858.14
## 2020.4904 42687.2922 2324.3666 83050.22 -19042.4755 104417.06
## 2020.4932 67910.0844 27469.2639 108350.90 6061.1866 129758.98
## 2020.4959 47455.0768 6936.5110 87973.64 -14512.7221 109422.88
## 2020.4986 40972.4950 376.3328 81568.66 -21113.9773 103058.97
## 2020.5014 58532.3989 17858.7884 99206.01 -3672.5204 120737.32
## 2020.5041 47739.4403 6988.5287 88490.35 -14583.7009 110062.58
## 2020.5068 45311.4093 4483.3429 86139.48 -17129.7299 107752.55
## 2020.5096 53815.9026 12910.8269 94720.98 -8743.0121 116374.82
## 2020.5123 65402.2667 24420.3265 106384.21 2725.7978 128078.74
## 2020.5151 44731.7796 3673.1187 85790.44 -18062.0235 107525.58
## 2020.5178 36072.3901 -5062.8483 77207.63 -26838.5282 98983.31
## 2020.5205 27413.0007 -13798.6730 68624.67 -35614.8153 90440.82
## 2020.5233 18753.6113 -22534.3562 60041.58 -44390.8859 81898.11
## 2020.5260 10094.2219 -31269.8987 51458.34 -53166.7414 73355.19
## 2020.5288 1434.8324 -40005.3012 42874.97 -61942.3828 64812.05
## 2020.5315 -7224.5570 -48740.5646 34291.45 -70717.8114 56268.70
## 2020.5342 47264.3041 5672.5611 88856.05 -16344.7777 110873.39
## 2020.5370 53204.3305 11536.9896 94871.67 -10520.3683 116929.03
## 2020.5397 40042.2572 -1700.5447 81785.06 -23797.8492 103882.36
## 2020.5425 45685.4156 3867.2889 87503.54 -18269.8902 109640.72
## 2020.5452 70711.9029 28818.5869 112605.22 6641.6050 134782.20
## 2020.5479 35305.1265 -6663.2441 77273.50 -28879.9575 99490.21
## 2020.5507 33780.2136 -8263.0777 75823.50 -30519.4517 98079.88
## 2020.5534 27057.1263 -15060.9524 69175.20 -37356.9164 91471.17
## 2020.5562 93393.8986 51201.1652 135586.63 28865.6812 157922.12
## 2020.5589 44140.0335 1872.7771 86407.29 -20502.1569 108782.22
## 2020.5616 53508.7734 11167.1251 95850.42 -11247.1895 118264.74
## 2020.5644 65119.4038 22703.4942 107535.31 249.8680 129988.94
## 2020.5671 52424.3148 9934.2737 94914.36 -12558.5954 117407.22
## 2020.5699 49879.7867 7315.7431 92443.83 -15216.3004 114975.87
## 2020.5726 69688.5536 27050.6361 112326.47 4479.4860 134897.62
## 2020.5753 83793.1183 41081.4545 126504.78 18471.2655 149114.97
## 2020.5781 65942.1938 23156.9110 108727.48 507.7504 131376.64
## 2020.5808 187714.0861 144855.3107 230572.86 122167.2454 253260.93
## 2020.5836 315933.2900 273001.1477 358865.43 250274.2444 381592.34
## 2020.5863 251525.6454 208520.2614 294531.03 185754.5863 317296.70
## 2020.5890 187118.0008 144039.4997 230196.50 121235.1187 253000.88
## 2020.5918 122710.3562 79558.8618 165861.85 56715.8405 188704.87
## 2020.5945 76722.0345 33497.6701 119946.40 10616.0738 142828.00
## 2020.5973 45960.7924 2663.6807 89257.90 -20256.4258 112178.01
## 2020.6000 51434.5393 8064.8023 94804.28 -14893.7497 117762.83
## 2020.6027 10169.3699 -33272.8711 53611.61 -56269.8043 76608.54
## 2020.6055 43652.2145 137.5904 87166.84 -22897.6601 110202.09
## 2020.6082 136001.5610 92414.6740 179588.45 69341.1698 202661.95
## 2020.6110 199841.8533 156182.8230 243500.88 133071.1284 266612.58
## 2020.6137 195160.4175 151429.3629 238891.47 128279.5410 262041.29
## 2020.6164 190478.9817 146676.0213 234281.94 123488.1347 257469.83
## 2020.6192 185797.5459 141922.7975 229672.29 118696.9086 252898.18
## 2020.6219 181116.1101 137169.6909 225062.53 113905.8618 248326.36
## 2020.6247 176434.6743 132416.7010 220452.65 109114.9936 243754.36
## 2020.6274 171753.2385 127663.8273 215842.65 104324.3029 239182.17
## 2020.6301 59258.0366 15097.3031 103418.77 -8279.9772 126796.05
## 2020.6329 30589.2588 -13642.6821 74821.20 -37057.6572 98236.17
## 2020.6356 32586.6638 -11716.3700 76889.70 -35168.9794 100342.31
## 2020.6384 42428.2626 -1945.7502 86802.28 -25435.9336 110292.46
## 2020.6411 47553.6406 3108.7621 91998.52 -20418.9353 115526.22
## 2020.6438 55625.1836 11109.5523 100140.81 -12455.5994 123705.97
## 2020.6466 42825.0612 -1761.2107 87411.33 -25363.7573 111013.88
## 2020.6493 30730.1543 -13926.6463 75386.95 -37566.5286 99026.84
## 2020.6521 93846.6542 49119.4359 138573.87 25442.2768 162251.03
## 2020.6548 104369.7490 59572.2238 149167.27 35857.8464 172881.65
## 2020.6575 63363.3428 18495.6208 108231.06 -5255.9164 131982.60
## 2020.6603 44584.5511 -353.2580 89522.36 -24141.8971 113311.00
## 2020.6630 73484.4441 28476.6571 118492.23 4650.9739 142317.91
## 2020.6658 95971.8656 50894.2093 141049.52 27031.5395 164912.19
## 2020.6685 105789.0068 60641.5893 150936.42 36741.9902 174836.02
## 2020.6712 77935.1382 32718.0672 123152.21 8781.5957 147088.68
## 2020.6740 127760.0385 82473.4211 173046.66 58500.1339 197019.94
## 2020.6767 123056.8096 77700.7523 168412.87 53690.7059 192422.91
## 2020.6795 155125.0832 109699.6923 200550.47 85652.9429 224597.22
## 2020.6822 207108.3905 161613.7716 252603.01 137530.3752 276686.41
## 2020.6849 214563.6459 168999.9042 260127.39 144879.9164 284247.38
## 2020.6877 233178.6758 187545.9160 278811.44 163389.3922 302967.96
## 2020.6904 250209.5955 204507.9219 295911.27 180314.9173 320104.27
## 2020.6932 160696.4940 114926.0103 206466.98 90696.5798 230696.41
## 2020.6959 142530.7465 96691.5560 188369.94 72425.7543 212635.74
## 2020.6986 109911.9018 64004.1073 155819.70 39701.9889 180121.81
## 2020.7014 159501.6523 113525.3562 205477.95 89186.9752 229816.33
## 2020.7041 191630.4052 145585.7094 237675.10 121211.1197 262049.69
## 2020.7068 170931.5174 124818.5233 217044.51 100407.7788 241455.26
## 2020.7096 166193.5398 120012.3485 212374.73 95565.5025 236821.58
## 2020.7123 161455.5622 115206.2742 207704.85 90723.3800 232187.74
## 2020.7151 156717.5845 110400.3000 203034.87 85881.4106 227553.76
## 2020.7178 151979.6069 105594.4255 198364.79 81039.5937 222919.62
## 2020.7205 147241.6293 100788.6503 193694.61 76197.9286 218285.33
## 2020.7233 142503.6517 95982.9738 189024.33 71356.4145 213650.89
## 2020.7260 187741.2694 141152.9910 234329.55 116490.6462 258991.89
## 2020.7288 229663.0578 183007.2769 276318.84 158309.1984 301016.92
## 2020.7315 165816.2784 119093.0926 212539.46 94359.3320 237273.22
## 2020.7342 115703.8503 68913.3565 162494.34 44143.9653 187263.74
## 2020.7370 92730.7535 45873.0485 139588.46 21068.0779 164393.43
## 2020.7397 81517.5490 34592.7291 128442.37 9752.2299 153282.87
## 2020.7425 73293.2525 26301.4135 120285.09 1425.4366 145161.07
## 2020.7452 129302.2632 82243.5006 176361.03 57332.0964 201272.43
## 2020.7479 136286.0400 89160.4487 183411.63 64213.6677 208358.41
## 2020.7507 171472.5858 124280.2606 218664.91 99298.1527 243647.02
## 2020.7534 197550.3209 150291.3560 244809.29 125273.9712 269826.67
## 2020.7562 191939.9439 144614.4331 239265.45 119561.8210 264318.07
## 2020.7589 174128.0215 126736.0582 221519.98 101648.2683 246607.77
## 2020.7616 153963.2878 106504.9651 201421.61 81382.0467 226544.53
## 2020.7644 178100.7242 130576.1348 225625.31 105418.1368 250783.31
## 2020.7671 198886.9864 151296.2225 246477.75 126103.1939 271670.78
## 2020.7699 215525.9779 167869.1314 263182.82 142641.1208 288410.83
## 2020.7726 199069.0869 151346.2494 246791.92 126083.3052 272054.87
## 2020.7753 199080.6769 151291.9394 246869.41 125994.1099 272167.24
## 2020.7781 245725.9469 197871.4001 293580.49 172538.7333 318913.16
## 2020.7808 270886.8447 222966.5792 318807.11 197599.1229 344174.57
## 2020.7836 274910.7298 226924.8355 322896.62 201522.6374 348298.82
## 2020.7863 240379.5239 192328.0903 288430.96 166891.1979 313867.85
## 2020.7890 219228.6807 171111.7973 267345.56 145640.2578 292817.10
## 2020.7918 233802.2010 185619.9565 281984.45 160113.8170 307490.58
## 2020.7945 234398.9697 186151.4528 282646.49 160610.7601 308187.18
## 2020.7973 222698.0738 174385.3726 271010.78 148810.1734 296585.97
## 2020.8000 214352.8735 165975.0758 262730.67 140365.4167 288340.33
## 2020.8027 181333.3795 132890.5729 229776.19 107246.5001 255420.26
## 2020.8055 180819.5642 132311.8357 229327.29 106633.3953 255005.73
## 2020.8082 180305.7489 131733.1853 228878.31 106020.4233 254591.07
## 2020.8110 179791.9335 131154.6213 228429.25 105407.5835 254176.28
## 2020.8137 179278.1182 130576.1434 227980.09 104794.8753 253761.36
## 2020.8164 178764.3029 129997.7513 227530.85 104182.2982 253346.31
## 2020.8192 178250.4876 129419.4445 227081.53 103569.8518 252931.12
## 2020.8219 172366.8052 123471.3557 221262.25 97587.6683 247145.94
## 2020.8247 195993.6137 147033.8426 244953.38 121116.1054 270871.12
## 2020.8274 200697.2677 151673.2593 249721.28 125721.5170 275673.02
## 2020.8301 200457.4096 151369.2481 249545.57 125383.5451 275531.27
## 2020.8329 137549.2329 88397.0019 186701.46 62377.3826 212721.08
## 2020.8356 191480.0892 142263.8722 240696.31 116210.3807 266749.80
## 2020.8384 212405.8292 163125.7092 261685.95 137038.3895 287773.27
## 2020.8411 212606.7105 163262.7703 261950.65 137141.6662 288071.75
## 2020.8438 208875.4381 159467.7601 258283.12 133312.9153 284437.96
## 2020.8466 131434.0079 81962.6743 180905.34 55774.1322 207093.88
## 2020.8493 163206.2673 113671.3598 212741.17 87449.1637 238963.37
## 2020.8521 206779.8719 157181.4721 256378.27 130925.6652 282634.08
## 2020.8548 211258.6337 161596.8227 260920.44 135307.4479 287209.82
## 2020.8575 251594.7128 201869.5714 301319.85 175546.6716 327642.75
## 2020.8603 191293.4962 141505.1051 241081.89 115148.7229 267438.27
## 2020.8630 145992.1055 96140.5448 195843.67 69750.7227 222233.49
## 2020.8658 191737.0671 141822.4168 241651.72 115399.1971 268074.94
## 2020.8685 41891.4091 -8086.2511 91869.07 -34542.8263 118325.64
## 2020.8712 225317.2124 175276.6216 275357.80 148786.7330 301847.69
## 2020.8740 300363.8640 250260.4216 350467.31 223737.2614 376990.47
## 2020.8767 302023.6891 251857.4739 352189.90 225301.0838 378746.29
## 2020.8795 236204.0190 185975.1095 286432.93 159385.5309 313022.51
## 2020.8822 224283.2288 173991.7030 274574.75 147368.9775 301197.48
## 2020.8849 192080.4352 141726.3711 242434.50 115070.5398 269090.33
## 2020.8877 190219.6377 139803.1129 240636.16 113114.2168 267325.06
## 2020.8904 154594.3443 104115.4360 205073.25 77393.5161 231795.17
## 2020.8932 166688.8130 116147.5982 217230.03 89392.6953 243984.93
## 2020.8959 172577.8065 121974.3620 223181.25 95186.5165 249969.10
## 2020.8986 175541.3930 124875.7951 226206.99 98055.0477 253027.74
## 2020.9014 172103.2344 121375.5593 222830.91 94521.9502 249684.52
## 2020.9041 151981.2969 101191.6205 202770.97 74305.1900 229657.40
## 2020.9068 142634.9101 91783.3080 193486.51 64864.0960 220405.72
## 2020.9096 159398.8728 108485.4203 210312.33 81533.4666 237264.28
## 2020.9123 135231.2052 84255.9774 186206.43 57271.3218 213191.09
## 2020.9151 139491.7495 88454.8211 190528.68 61437.5032 217546.00
## 2020.9178 123327.7796 72229.2252 174426.33 45179.2844 201476.27
## 2020.9205 121503.9204 70343.8141 172664.03 43261.2897 199746.55
## 2020.9233 142752.1906 91530.6064 193973.77 64415.5376 221088.84
## 2020.9260 168416.6828 117133.6944 219699.67 89986.1202 246847.25
## 2020.9288 172105.2626 120760.9435 223449.58 93580.9028 250629.62
## 2020.9315 115197.9315 63792.3548 166603.51 36579.8863 193815.98
## 2020.9342 41762.7855 -9703.9758 93229.55 -36948.8335 120474.40
## 2020.9370 25379.9440 -26147.9294 76907.82 -53425.1378 104185.03
## 2020.9397 44940.7356 -6648.1773 96529.65 -33957.6981 123839.17
## 2020.9425 24170.9573 -27478.9231 75820.84 -54820.7182 103162.63
## 2020.9452 57633.2133 5922.4373 109343.99 -21451.5939 136718.02
## 2020.9479 45351.5403 -6420.0597 97123.14 -33826.2892 124529.37
## 2020.9507 75569.0992 23736.7467 127401.45 -3701.6433 154839.84
## 2020.9534 74260.5085 22367.4745 126153.54 -5103.0383 153624.06
## 2020.9562 85460.4775 33506.8329 137414.12 6004.2347 164916.72
## 2020.9589 89882.1890 37868.0045 141896.37 10333.3584 169431.02
## 2020.9616 90001.4528 37926.7987 142076.11 10360.1420 169642.76
## 2020.9644 85696.4547 33561.4011 137831.51 5962.7709 165430.14
## 2020.9671 87887.8819 35692.4988 140083.27 8061.9320 167713.83
## 2020.9699 31276.4918 -20979.1513 83532.13 -48641.6177 111194.60
## 2020.9726 41702.0279 -10613.8057 94017.86 -38308.1350 121712.19
## 2020.9753 18159.0729 -34216.8820 70535.03 -61943.0377 98261.18
## 2020.9781 12878.2613 -39557.7459 65314.27 -67315.6914 93072.21
## 2020.9808 39728.1430 -12767.8480 92224.13 -40557.5469 120013.83
## 2020.9836 40894.9677 -11660.9385 93450.87 -39482.3546 121272.29
## 2020.9863 57907.6245 5291.8714 110523.38 -22561.2259 138376.47
## 2020.9890 43567.9637 -9107.5685 96243.50 -36992.3108 124128.24
## 2020.9918 58859.4498 6124.2064 111594.69 -21792.1451 139511.04
## 2020.9945 82292.3674 29497.4803 135087.25 1549.5552 163035.18
## 2020.9973 55100.8301 2246.3666 107955.29 -25733.0963 135934.76
## 2021.0000 30364.6599 -22549.3130 83278.63 -50560.2782 111289.60
## 2021.0027 54936.5397 1963.1244 107909.96 -26079.3077 135952.39
## 2021.0055 94256.1140 41223.3229 147288.91 13149.4590 175362.77
## 2021.0082 87003.0923 33910.9917 140095.19 5805.7314 168200.45
## 2021.0110 79377.4509 26226.1070 132528.79 -1910.5148 160665.42
## 2021.0137 48159.1930 -5051.3281 101369.71 -33219.2766 129537.66
## 2021.0164 31112.9502 -22156.6826 84382.58 -50355.9228 112581.82
## 2021.0192 70500.3055 17171.6267 123828.98 -11058.8706 152059.48
## 2021.0219 85807.4267 32419.7672 139195.09 4158.0474 167456.81
## 2021.0247 39973.9975 -13472.5776 93420.57 -41765.4855 121713.48
## 2021.0274 35058.4628 -18446.9632 88563.89 -46771.0247 116887.95
## 2021.0301 37696.5202 -15867.6919 91260.73 -44222.8729 119615.91
## 2021.0329 60433.1606 6810.2269 114056.09 -21576.0396 142442.36
## 2021.0356 44704.1496 -8977.4416 98385.74 -37394.7594 126803.06
## 2021.0384 34559.1616 -19181.0230 88299.35 -47629.3583 116747.68
## 2021.0411 17112.7999 -36685.9143 70911.51 -65165.2333 99390.83
## 2021.0438 42800.1987 -11056.9815 96657.38 -39567.2505 125167.65
## 2021.0466 50217.4755 -3698.1073 104133.06 -32239.2928 132674.24
## 2021.0493 86696.2478 32722.3257 140670.17 4150.2572 169242.24
## 2021.0521 41601.6588 -12430.5398 95633.86 -41033.4579 124236.78
## 2021.0548 72272.7610 18182.3488 126363.17 -10451.3858 154996.91
## 2021.0575 71840.2690 17691.7058 125988.83 -10972.8121 154653.35
## 2021.0603 79381.4352 25174.7833 133588.09 -3520.4848 162283.36
## 2021.0630 68638.1003 14373.4220 122902.78 -14352.5635 151628.76
## 2021.0658 60470.2419 6147.5991 114792.88 -22609.0710 143549.55
## 2021.0685 56867.2326 2486.6871 111247.78 -26300.6348 140035.10
## 2021.0712 55021.9985 583.6119 109460.39 -28234.3293 138278.33
## 2021.0740 44771.2984 -9724.8680 99267.46 -38573.3958 128115.99
## 2021.0767 84361.2512 29807.3663 138915.14 928.2841 167794.22
## 2021.0795 81475.2993 26863.7569 136086.84 -2045.8474 164996.45
## 2021.0822 72024.3531 17355.2139 126693.49 -11584.8802 155633.59
## 2021.0849 81535.4579 26808.7827 136262.13 -2161.7692 165232.69
## 2021.0877 118715.8723 63931.7213 173500.02 34930.7437 202501.00
## 2021.0904 80193.4877 25351.9214 135035.05 -3679.4502 164066.43
## 2021.0932 64219.2819 9320.3602 119118.20 -19741.3735 148179.94
## 2021.0959 96185.3553 41229.1380 151141.57 12137.0739 180233.64
## 2021.0986 78745.9041 23732.4509 133759.36 -5389.9120 162881.72
## 2021.1014 52655.6261 -2415.0034 107726.26 -31567.6337 136878.89
## 2021.1041 36907.9762 -18219.7704 92035.72 -47402.6366 121218.59
## 2021.1068 30920.3325 -24264.4720 86105.14 -53477.5429 115318.21
## 2021.1096 50916.3887 -4325.4149 106158.19 -33568.6592 135401.44
## 2021.1123 28151.2701 -27147.4737 83450.01 -56420.8604 112723.40
## 2021.1151 38167.5709 -17188.0546 93523.20 -46491.5526 122826.69
## 2021.1178 93492.7086 38080.2598 148905.16 8746.6813 178238.74
## 2021.1205 67393.8233 11924.6094 122863.04 -17439.0187 152226.67
## 2021.1233 69552.5887 14026.6677 125078.51 -15366.9793 154472.16
## 2021.1260 90925.5032 35342.9330 146508.07 5919.2977 175931.71
## 2021.1288 106423.8035 50784.6418 162062.97 21331.0488 191516.56
## 2021.1315 74978.1713 19282.4756 130673.87 -10201.0448 160157.39
## 2021.1342 67799.2266 12047.0541 123551.40 -17466.3632 153064.82
## 2021.1370 79760.0373 23951.4453 135568.63 -5591.8388 165111.91
## 2021.1397 82295.1987 26430.2441 138160.15 -3142.8765 167733.27
## 2021.1425 104500.8443 48579.5840 160422.10 18976.6569 190025.03
## 2021.1452 66672.1686 10694.6591 122649.68 -18938.0445 152282.38
## 2021.1479 69698.6685 13664.9664 125732.37 -15997.4838 155394.82
## 2021.1507 80773.9006 24684.0621 136863.74 -5008.1048 166555.91
## 2021.1534 63784.0994 7638.1807 119930.02 -22083.6733 149651.87
## 2021.1562 41776.6136 -14425.3294 97978.56 -44176.8409 127730.07
## 2021.1589 45293.9533 -10963.9582 101551.86 -40745.0976 131333.00
## 2021.1616 50949.9706 -5363.8537 107263.80 -35174.5917 137074.53
## 2021.1644 78424.3049 22054.6231 134793.99 -7785.6839 164634.29
## 2021.1671 79745.6135 23320.1296 136171.10 -6549.7173 166040.94
## 2021.1699 78333.9406 21852.7097 134815.17 -8046.6478 164714.53
## 2021.1726 66028.0308 9491.1079 122564.95 -20437.7312 152493.79
## 2021.1753 76953.0843 20360.5242 133545.64 -9597.7675 163503.94
## 2021.1781 74026.5032 17378.3605 130674.65 -12609.3548 160662.36
## 2021.1808 87300.8531 30597.1823 144004.52 580.0722 174021.63
## 2021.1836 84530.8166 27771.6721 141289.96 -2274.8040 171336.44
## 2021.1863 55607.4353 -1207.1288 112422.00 -31282.9423 142497.81
## 2021.1890 77715.8617 20845.9321 134585.79 -9259.1902 164690.91
## 2021.1918 65007.8775 8082.6361 121933.12 -22051.7665 152067.52
## 2021.1945 69356.2801 12375.7806 126336.78 -17787.8738 156500.43
## 2021.1973 84063.7528 27028.0489 141099.46 -3164.8290 171292.33
## 2021.2000 103072.3244 45981.4693 160163.18 15759.3962 190385.25
## 2021.2027 32167.1373 -24978.8157 89313.09 -55230.0559 119564.33
## 2021.2055 68878.2925 11677.2947 126079.29 -18603.0844 156359.67
## 2021.2082 53648.8087 -3607.1810 110904.80 -33916.6711 141214.29
## 2021.2110 42265.5770 -15045.3519 99576.51 -45383.9250 129915.08
## 2021.2137 79044.1030 21678.2876 136409.92 -8689.3407 166777.55
## 2021.2164 55062.5869 -2358.0626 112483.24 -32754.7183 142879.89
## 2021.2192 66701.6516 9226.2204 124177.08 -21199.4350 154602.74
## 2021.2219 99976.9670 42446.8062 157507.13 11992.1786 187961.76
## 2021.2247 73762.3326 16177.4942 131347.17 -14306.0778 161830.74
## 2021.2274 63789.5180 6150.0540 121428.98 -24362.4352 151941.47
## 2021.2301 62344.8008 4650.7627 120038.84 -25890.6162 150580.22
## 2021.2329 49179.1714 -8569.3891 106927.73 -39139.6304 137497.97
## 2021.2356 70826.4583 13023.4269 128629.49 -17575.6496 159228.57
## 2021.2384 87335.9551 29478.5040 145193.41 -1149.3806 175821.29
## 2021.2411 71099.5370 13187.7173 129011.36 -17468.9482 159668.02
## 2021.2438 56935.8155 -1030.3218 114901.95 -31715.7413 145587.37
## 2021.2466 80446.9168 22426.5129 138467.32 -8287.6337 169181.47
## 2021.2493 79717.5259 21642.9059 137792.15 -9099.9409 168534.99
## 2021.2521 67579.3613 9450.5759 125708.15 -21320.9444 156479.67
## 2021.2548 90951.8198 32768.9193 149134.72 1968.7523 179934.89
## 2021.2575 88607.8305 30370.8653 146844.80 -457.9218 177673.58
## 2021.2603 97227.7005 38936.7208 155518.68 8079.3401 186376.06
## 2021.2630 71308.9528 12964.0085 129653.90 -17921.9394 160539.84
## 2021.2658 50774.4499 -7624.4091 109173.31 -38538.8977 140087.80
## 2021.2685 74899.4117 16446.6876 133352.14 -14496.3153 164295.14
## 2021.2712 103302.2398 44795.7003 161808.78 13824.2092 192780.27
## 2021.2740 80221.5155 21661.2102 138781.82 -9338.7429 169781.77
## 2021.2767 102445.1597 43831.1378 161059.18 12802.7488 192087.57
## 2021.2795 92564.5410 33896.8516 151232.23 2840.0528 182289.03
## 2021.2822 92790.8672 34069.5594 151512.18 2984.3768 182597.36
## 2021.2849 68135.2390 9360.3618 126910.12 -21753.1788 158023.66
## 2021.2877 63812.2007 4983.8027 122640.60 -26158.0700 153782.47
## 2021.2904 81203.3985 22321.5285 140085.27 -8848.6506 171255.45
## 2021.2932 64235.6688 5300.3753 123170.96 -25898.0845 154369.42
## 2021.2959 54832.3663 -4156.3023 113821.03 -35383.0173 145047.75
## 2021.2986 67852.2154 8810.2198 126894.21 -22444.7246 158149.16
## 2021.3014 94854.3363 35759.0620 153949.61 4475.9134 185232.76
## 2021.3041 70424.8486 11276.3435 129573.35 -20034.9838 160884.68
## 2021.3068 55819.0273 -3382.6607 115020.72 -34722.1413 146360.20
## 2021.3096 65356.5010 6101.6778 124611.32 -25265.9308 155978.93
## 2021.3123 92675.5291 33367.6183 151983.44 1971.9068 183379.15
## 2021.3151 157191.1885 97830.2376 216552.14 66406.4484 247975.93
## 2021.3178 119654.8776 60240.9339 179068.82 28789.0920 210520.66
## 2021.3205 65166.0426 5699.1535 124632.93 -25780.7161 156112.80
## 2021.3233 50333.5157 -9186.2719 109853.30 -40694.1442 141361.18
## 2021.3260 73443.3860 13870.7470 133016.03 -17665.1032 164551.88
## 2021.3288 108168.2599 48542.8163 167793.70 16979.0130 199357.51
## 2021.3315 70526.9986 10848.7971 130205.20 -20742.9345 161796.93
## 2021.3342 60510.5206 779.6078 120241.43 -30840.0274 151861.07
## 2021.3370 90426.8555 30643.2778 150210.43 -1004.2365 181857.95
## 2021.3397 107745.2110 47909.0149 167581.41 16233.6460 199256.78
## 2021.3425 95031.9909 35143.2226 154920.76 3440.0237 186623.96
## 2021.3452 81765.4952 21824.2007 141706.79 -9906.8038 173437.79
## 2021.3479 66432.5872 6438.8127 126426.36 -25319.9732 158185.15
## 2021.3507 58048.5187 -1997.6901 118094.73 -33784.2330 149881.27
## 2021.3534 75280.1488 15181.5514 135378.75 -16632.7243 167193.02
## 2021.3562 110537.4646 50386.5244 170688.40 18544.5400 202530.39
## 2021.3589 136048.6299 75845.3923 196251.87 43975.7234 228121.54
## 2021.3616 113640.2934 53384.8037 173895.78 21487.4743 205793.11
## 2021.3644 86886.7687 26579.0724 147194.47 -5345.8936 179119.43
## 2021.3671 104436.0641 44076.2062 164795.92 12123.6276 196748.50
## 2021.3699 48578.6790 -11833.2955 108990.65 -43813.4630 140970.82
## 2021.3726 37331.6134 -23132.4327 97795.66 -55140.1652 129803.39
## 2021.3753 25876.0748 -34639.9981 86392.15 -66675.2719 118427.42
## 2021.3781 44645.6289 -15922.4261 105213.68 -47985.2176 137276.48
## 2021.3808 93115.3642 32495.3717 153735.36 405.0861 185825.64
## 2021.3836 107956.4507 47284.5652 168628.34 15166.8090 200746.09
## 2021.3863 92858.6696 32134.9353 153582.40 -10.2679 185727.61
## 2021.3890 87231.7407 26456.2019 148007.28 -5716.4249 180179.91
## 2021.3918 78317.4308 17490.1317 139144.73 -14709.8954 171344.76
## 2021.3945 84262.5360 23383.5205 145141.55 -8843.8836 177368.96
## 2021.3973 51832.5489 -9098.1391 112763.24 -41352.8970 145017.99
## 2021.4000 45452.3056 -15530.0111 106434.62 -47812.0995 138716.71
## 2021.4027 25391.5617 -35642.3400 86425.46 -67951.7359 118734.86
## 2021.4055 62020.3581 934.9149 123105.80 -31401.7653 155442.48
## 2021.4082 76925.2724 15788.3313 138062.21 -16575.6104 170426.16
## 2021.4110 115231.6438 54043.2480 176420.04 21652.0678 208811.22
## 2021.4137 39552.6591 -21687.1482 100792.47 -54105.5439 133210.86
## 2021.4164 44595.1801 -16695.9955 105886.36 -49141.5839 138331.94
## 2021.4192 47541.7582 -13800.7426 108884.26 -46273.5010 141357.02
## 2021.4219 71223.5844 9829.8012 132617.37 -22670.1044 165117.27
## 2021.4247 64456.3388 3011.3160 125901.36 -29515.7142 158428.39
## 2021.4274 64160.0879 2663.8682 125656.31 -29890.2640 158210.44
## 2021.4301 53716.9249 -7830.4490 115264.30 -40411.6607 147845.51
## 2021.4329 44199.5583 -17398.9275 105798.04 -50007.1962 138406.31
## 2021.4356 57026.9972 -4622.5580 118676.55 -37257.8612 151311.86
## 2021.4384 63616.1753 1915.5929 125316.76 -30746.7224 157979.07
## 2021.4411 65412.5104 3660.9430 127164.08 -29028.3622 159853.38
## 2021.4438 90540.7507 28738.2404 152343.26 -3978.0323 185059.53
## 2021.4466 98127.9354 36274.5241 159981.35 3531.3060 192724.56
## 2021.4493 123163.0825 61258.8120 185067.35 28488.6707 217837.49
## 2021.4521 87826.7186 25871.6307 149781.81 -6925.4117 182578.85
## 2021.4548 89580.9064 27575.0429 151586.77 -5248.8786 184410.69
## 2021.4575 52044.8452 -10011.7526 114101.44 -42862.5311 146952.22
## 2021.4603 78135.5145 16028.2240 140242.81 -16849.3896 173120.42
## 2021.4630 69025.3437 6867.4018 131183.29 -26037.0250 164087.71
## 2021.4658 60303.4043 -1905.1478 122511.96 -34836.3660 155443.17
## 2021.4685 48575.6295 -13683.4916 110834.75 -46641.4795 143792.74
## 2021.4712 59607.2034 -2702.4457 121916.85 -35687.1815 154901.59
## 2021.4740 65929.0659 3568.9298 128289.20 -29442.5322 161300.66
## 2021.4767 73335.2702 10924.6879 135745.85 -22113.4787 168784.02
## 2021.4795 70168.6594 7707.6717 132629.65 -25357.1780 165694.50
## 2021.4822 47041.5574 -15469.7952 109552.91 -48561.3064 142644.42
## 2021.4849 38910.3350 -23651.3419 101472.01 -56769.4931 134590.16
## 2021.4877 77290.7248 14678.7641 139902.69 -18466.0057 173047.46
## 2021.4904 68000.8350 5338.6309 130663.04 -27832.7362 163834.41
## 2021.4932 39932.0231 -22780.3843 102644.43 -55978.3274 135842.37
## 2021.4959 35162.9599 -27599.6105 97925.53 -60824.1083 131150.03
## 2021.4986 65566.3927 2753.6993 128379.09 -30497.3320 161630.12
## 2021.5014 54115.7237 -8747.0528 116978.50 -42024.5965 150256.04
## 2021.5041 39336.8472 -23575.9723 102249.67 -56880.0073 135553.70
## 2021.5068 52136.2340 -10826.5890 115099.06 -44157.0941 148429.56
## 2021.5096 70995.9923 7983.2056 134008.78 -25373.7487 167365.73
## 2021.5123 46894.7381 -16167.9727 109957.45 -49551.3552 143340.83
## 2021.5151 53160.1408 -9952.4547 116272.74 -43362.2446 149682.53
## 2021.5178 47227.5736 -15934.8671 110390.01 -49371.0434 143826.19
## 2021.5205 50455.2831 -12756.9635 113667.53 -46219.5055 147130.07
## 2021.5233 55398.9851 -7863.0282 118661.00 -41351.9151 152149.89
## 2021.5260 42671.7467 -20639.9942 105983.49 -54155.2053 139498.70
## 2021.5288 58561.3746 -4800.0548 121922.80 -38341.5695 155464.32
## 2021.5315 63305.9070 -105.1721 126716.99 -33672.9697 160284.78
## 2021.5342 58078.9582 -5381.7317 121539.65 -38975.7917 155133.71
## 2021.5370 45749.7627 -17760.4992 109260.02 -51380.8010 142880.33
## 2021.5397 48550.3577 -15009.4376 112110.15 -48655.9608 145756.68
## 2021.5425 54835.2725 -8774.0176 118444.56 -42446.7418 152117.29
## 2021.5452 60526.8919 -3131.8545 124185.64 -36830.7593 157884.54
## 2021.5479 35443.2241 -28264.9403 99151.39 -61990.0053 132876.45
## 2021.5507 43331.3477 -20426.1963 107088.89 -54177.4013 140840.10
## 2021.5534 49998.3300 -13808.5554 113805.22 -47585.8802 147582.54
## 2021.5562 69294.0384 5437.8498 133150.23 -28365.5746 166953.65
## 2021.5589 71203.4146 7297.9607 135108.87 -26531.5431 168938.37
## 2021.5616 45079.2811 -18875.4001 109033.96 -52730.9633 142889.53
## 2021.5644 74569.3850 10565.5144 138573.26 -23316.0881 172454.86
## 2021.5671 46811.2550 -17241.7672 110864.28 -51149.3890 144771.90
## 2021.5699 33193.4501 -30908.6861 97295.59 -64842.3072 131229.21
## 2021.5726 104260.6110 40109.3984 168411.82 6149.7978 202371.42
## 2021.5753 119237.1399 55036.8885 183437.39 21051.3282 217422.95
## 2021.5781 177544.2813 113295.0284 241793.53 79283.5284 275805.03
## 2021.5808 131460.6229 67162.4060 195758.84 33124.9860 229796.26
## 2021.5836 84062.8375 19715.6937 148409.98 -14347.6266 182473.30
## 2021.5863 61164.3378 -3231.6957 125560.37 -37320.8966 159649.57
## 2021.5890 67408.3827 2963.4967 131853.27 -31151.5652 165968.33
## 2021.5918 129321.7444 64828.0428 193815.45 30687.1395 227956.35
## 2021.5945 138400.4733 73857.9932 202942.95 39691.2680 237109.68
## 2021.5973 115283.5979 50692.3759 179874.82 16499.8484 214067.35
## 2021.6000 54741.5667 -9898.3603 119381.49 -44116.6707 153599.80
## 2021.6027 69176.4427 4487.8473 133865.04 -29756.2265 168109.11
## 2021.6055 49375.6151 -15361.6121 114112.84 -49631.4301 148382.66
## 2021.6082 77969.5246 13183.7022 142755.35 -21111.8406 177050.89
## 2021.6110 60276.2015 -4558.1798 125110.58 -38879.4281 159431.83
## 2021.6137 78084.5495 13201.6457 142967.45 -21145.2888 177314.39
## 2021.6164 35084.1046 -29847.2854 100015.49 -64219.8870 134388.10
## 2021.6192 50944.6589 -14035.1812 115924.50 -48433.4307 150322.75
## 2021.6219 46003.3358 -19024.9183 111031.59 -53448.7966 145455.47
## 2021.6247 43525.0171 -21551.6150 108601.65 -56001.1030 143051.14
## 2021.6274 26850.4218 -38274.5522 91975.40 -72749.6310 126450.47
## 2021.6301 54104.4845 -11068.7957 119277.76 -45569.4462 153778.42
## 2021.6329 37089.3075 -28132.2431 102310.86 -62658.4464 136837.06
## 2021.6356 54708.3199 -10561.4654 119978.11 -45113.2026 154529.84
## 2021.6384 51710.4413 -13607.5431 117028.43 -48184.7953 151605.68
## 2021.6411 72287.3849 6921.2370 137653.53 -27681.5115 172256.28
## 2021.6438 50861.8686 -14552.4074 116276.14 -49180.6333 150904.37
## 2021.6466 -13364.5089 -78826.8775 52097.86 -113480.5622 86751.54
## 2021.6493 12750.5652 -52759.8608 78260.99 -87438.9855 112940.12
## 2021.6521 40913.6571 -24644.7911 106472.11 -59349.3372 141176.65
## 2021.6548 47976.2952 -17630.1400 113582.73 -52360.0888 148312.68
## 2021.6575 91833.0260 26178.6389 157487.41 -8576.6942 192242.75
## 2021.6603 70198.7826 4496.4786 135901.09 -30284.2202 170681.79
## 2021.6630 119165.9106 53415.7246 184916.10 18609.6786 219722.14
## 2021.6658 99441.0283 33642.9952 165239.06 -1188.3795 200070.44
## 2021.6685 88061.9719 22216.1264 153907.82 -12640.5587 188764.50
## 2021.6712 66191.7568 298.1336 132085.38 -34583.8435 166967.36
## 2021.6740 49286.6318 -16654.7345 115228.00 -51561.9852 150135.25
## 2021.6767 54286.7697 -11702.3051 120275.84 -46634.8112 155208.35
## 2021.6795 38277.7916 -27758.9573 104314.54 -62716.7006 139272.28
## 2021.6822 95336.3916 29252.0030 161420.78 -5730.9592 196403.74
## 2021.6849 50170.0890 -15961.9049 116302.08 -50970.0678 151310.25
## 2021.6877 74821.3611 8641.7961 141000.93 -26391.5495 176034.27
## 2021.6904 144956.0403 78728.9383 211183.14 43670.4282 246241.65
## 2021.6932 124146.2143 57871.6095 190420.82 22787.9529 225504.48
## 2021.6959 162120.9995 95798.9258 228443.07 60690.1407 263551.86
## 2021.6986 172961.0174 106591.5088 239330.53 71457.6133 274464.42
## 2021.7014 147878.0281 81461.1186 214294.94 46302.1305 249453.93
## 2021.7041 160038.2406 93573.9638 226502.52 58389.9010 261686.58
## 2021.7068 148081.5397 81569.9295 214593.15 46360.8098 249802.27
## 2021.7096 157293.8679 90734.9579 223852.78 55500.7993 259086.94
## 2021.7123 168766.1797 102160.0035 235372.36 66900.8237 270631.54
## 2021.7151 127343.1602 60689.7513 193996.57 25405.5680 229280.75
## 2021.7178 91906.8838 25206.2757 158607.49 -10102.8934 193916.66
## 2021.7205 84561.7349 17813.9609 151309.51 -17520.1763 186643.65
## 2021.7233 90540.2510 23745.3444 157335.16 -11613.7432 192694.25
## 2021.7260 112752.6110 45910.6051 179594.62 10526.5846 214978.64
## 2021.7288 171615.2908 104726.2187 238504.36 69317.2829 273913.30
## 2021.7315 204991.5228 138055.4177 271927.63 102621.5841 307361.46
## 2021.7342 232205.8221 165222.7170 299188.93 129764.0030 334647.64
## 2021.7370 217955.7950 150925.7227 284985.87 115442.1459 320469.44
## 2021.7397 224272.0892 157195.0828 291349.10 121686.6605 326857.52
## 2021.7425 198228.5522 131104.6444 265352.46 95571.3940 300885.71
## 2021.7452 219493.7497 152322.9733 286664.53 116764.9121 322222.59
## 2021.7479 206203.8208 138986.2084 273421.43 103403.3538 309004.29
## 2021.7507 211997.2236 144732.8079 279261.64 109125.1771 314869.27
## 2021.7534 203830.8614 136519.6749 271142.05 100887.2851 306774.44
## 2021.7562 203179.9682 135822.0433 270537.89 100164.9118 306195.02
## 2021.7589 202681.1543 135276.5235 270085.79 99594.6674 305767.64
## 2021.7616 205896.5772 138445.2729 273347.88 102738.7092 309054.45
## 2021.7644 201276.2600 133778.3144 268774.21 98047.0603 304505.46
## 2021.7671 209338.8747 141794.3200 276883.43 106038.3926 312639.36
## 2021.7699 207917.1904 140326.0587 275508.32 104545.4749 311288.91
## 2021.7726 126005.3999 58367.7233 193643.08 22562.5002 229448.30
## 2021.7753 116724.1475 49039.9580 184408.34 13210.1125 220238.18
## 2021.7781 133840.8740 66110.2036 201571.54 30255.7525 237426.00
## 2021.7808 133363.0564 65585.9369 201140.18 29706.8972 237019.22
## 2021.7836 117181.8962 49358.3596 185005.43 13454.7480 220909.04
## 2021.7863 112330.9197 44460.9975 180200.84 8532.8310 216129.01
## 2021.7890 111436.7584 43520.4824 179353.03 7567.7776 215305.74
## 2021.7918 87744.7668 19782.1686 155707.37 -16195.0576 191684.59
## 2021.7945 60888.1878 -7120.7010 128897.08 -43122.4321 164898.81
## 2021.7973 40103.7348 -27951.4132 108158.88 -63977.6323 144185.10
## 2021.8000 81380.1967 13278.8210 149481.57 -22771.8697 185532.26
## 2021.8027 142786.7684 74639.1963 210934.34 38564.0507 247009.49
## 2021.8055 148566.9822 80373.2450 216760.72 44273.6611 252860.30
## 2021.8082 174512.9955 106273.1244 242752.87 70149.1188 278876.87
## 2021.8110 186283.5644 117997.5906 254569.54 81849.1797 290717.95
## 2021.8137 236533.8775 168201.8322 304865.92 132029.0324 341038.72
## 2021.8164 215385.4564 147007.3706 283763.54 110810.1984 319960.71
## 2021.8192 203138.0117 134713.9163 271562.11 98492.3881 307783.64
## 2021.8219 193658.1893 125188.1152 262128.26 88942.2475 298374.13
## 2021.8247 190616.2335 122100.2117 259132.26 85830.0206 295402.45
## 2021.8274 215355.4034 146793.4645 283917.34 110498.9665 320211.84
## 2021.8301 173833.7458 105225.9206 242441.57 68907.1319 278760.36
## 2021.8329 215428.7321 146775.0513 284082.41 110431.9881 320425.48
## 2021.8356 239938.1839 171238.6782 308637.69 134871.3567 345005.01
## 2021.8384 304656.1298 235910.8297 373401.43 199519.2660 409792.99
## 2021.8411 332223.7335 263432.6694 401014.80 227016.8798 437430.59
## 2021.8438 286137.3332 217300.5356 354974.13 180860.5360 391414.13
## 2021.8466 256944.4726 188061.9717 325826.97 151597.7784 362291.17
## 2021.8493 205261.3097 136333.1360 274189.48 99844.7649 310677.85
## 2021.8521 217500.8848 148527.0685 286474.70 112014.5357 322987.23
## 2021.8548 217447.2047 148427.7760 286466.63 111891.0974 323003.31
## 2021.8575 183797.5058 114732.4947 252862.52 78171.6863 289423.33
## 2021.8603 175366.9427 106256.3793 244477.51 69671.4571 281062.43
## 2021.8630 162550.0952 93394.0097 231706.18 56784.9894 268315.20
## 2021.8658 167031.6718 97830.0940 236233.25 61196.9915 272866.35
## 2021.8685 125012.5469 55765.5066 194259.59 19108.3378 230916.76
## 2021.8712 105042.8653 35750.3925 174335.34 -930.8269 211016.56
## 2021.8740 84909.1654 15571.2897 154247.04 -21133.9645 190952.30
## 2021.8767 77100.9018 7717.6530 146484.15 -29011.6202 183213.42
## 2021.8795 99913.0666 30484.4743 169341.66 -6268.8023 206094.94
## 2021.8822 107538.3809 38064.4748 177012.29 1287.2104 213789.55
## 2021.8849 94100.0431 24580.8527 163619.23 -12220.3837 200420.47
## 2021.8877 160417.0205 90852.5753 229981.47 54027.3824 266806.66
## 2021.8904 155331.2322 85721.5615 224940.90 48872.4278 261790.04
## 2021.8932 162142.1713 92487.3045 231797.04 55614.2454 268670.10
## 2021.8959 128848.9822 59148.9487 198549.02 22251.9797 235445.98
## 2021.8986 140650.7432 70905.5722 210395.91 33984.7089 247316.78
## 2021.9014 87518.7345 17728.4552 157309.01 -19216.2870 194253.76
## 2021.9041 133659.0367 63823.6782 203494.40 26855.0726 240463.00
## 2021.9068 196207.0984 126326.6898 266087.51 89334.2361 303079.96
## 2021.9096 167588.1831 97662.7535 237513.61 60646.4670 274529.90
## 2021.9123 109162.4243 39192.0025 179132.85 2151.8987 216172.95
## 2021.9151 185016.8207 115001.4358 255032.21 77937.5298 292096.11
## 2021.9178 198670.1132 128609.7939 268730.43 91522.1012 305818.13
## 2021.9205 211400.9739 141295.7491 281506.20 104184.2848 318617.66
## 2021.9233 237095.4852 166945.3836 307245.59 129810.1630 344380.81
## 2021.9260 236157.9670 165963.0173 306352.92 128804.0555 343511.88
## 2021.9288 199921.9254 129682.1562 270161.69 92499.4685 307344.38
## 2021.9315 203533.8898 133249.3298 273818.45 96042.9311 311024.85
## 2021.9342 213899.8088 143570.4864 284229.13 106340.3920 321459.23
## 2021.9370 150202.5781 79828.5218 220576.63 42574.7468 257830.41
## 2021.9397 142997.4243 72578.6626 213416.19 35301.2219 250693.63
## 2021.9425 163692.8027 93229.3639 234156.24 55928.2726 271457.33
## 2021.9452 156853.3490 86345.2614 227361.44 49020.5344 264686.16
## 2021.9479 92718.6973 22165.9891 163271.41 -15182.3585 200619.75
## 2021.9507 122071.2869 51473.9864 192668.59 14102.0330 230040.54
## 2021.9534 80400.5143 9758.6496 151042.38 -27636.8947 188437.92
## 2021.9562 71553.5454 867.1446 142239.95 -36551.9757 179659.07
## 2021.9589 67716.7128 -3014.1961 138447.62 -40456.8775 175890.30
## 2021.9616 22203.3491 -48572.0398 92978.74 -86038.2675 130444.97
## 2021.9644 40714.7966 -30105.0444 111534.64 -67594.8037 149024.40
## 2021.9671 35774.5517 -35089.7136 106638.82 -72602.9896 144152.09
## 2021.9699 2312.5890 -68596.0727 73221.25 -106132.8507 110758.03
## 2021.9726 32318.1541 -38634.8762 103271.18 -76195.1416 140831.45
## 2021.9753 39305.9455 -31691.4256 110303.32 -69275.1637 147887.05
## 2021.9781 47414.9043 -23626.7801 118456.59 -61233.9762 156063.78
## 2021.9808 22580.4431 -48505.5269 93666.41 -86136.1664 131297.05
## 2021.9836 8224.7185 -62905.5095 79354.95 -100559.5777 117009.01
## 2021.9863 29293.2245 -41881.2340 100467.68 -79558.7164 138145.17
## 2021.9890 42155.0928 -29063.5688 113373.75 -66764.4509 151074.64
## 2021.9918 42470.1754 -28792.6618 113733.01 -66516.9290 151457.28
## 2021.9945 28429.7920 -42877.1935 99736.78 -80624.8314 137484.42
## 2021.9973 29556.6467 -41794.4597 100907.75 -79565.4538 138678.75
## 2022.0000 16547.0406 -54848.1595 87942.24 -92642.4954 125736.58
## 2022.0027 17081.9929 -54357.2736 88521.26 -92174.9369 126338.92
## 2022.0055 16122.7923 -55360.5135 87606.10 -93201.4898 125447.07
## 2022.0082 24155.6144 -47371.7036 95682.93 -85235.9785 133547.21
## 2022.0110 24419.5048 -47151.7983 95990.81 -85039.3575 133878.37
## 2022.0137 10981.8293 -60633.4318 82597.09 -98544.2611 120507.92
## 2022.0164 20568.0245 -51091.1678 92227.22 -89025.2528 130161.30
## 2022.0192 12783.1981 -58919.8984 84486.29 -96877.2248 122443.62
## 2022.0219 13425.6011 -58321.3728 85172.57 -96301.9265 123153.13
## 2022.0247 31383.3622 -40407.4622 103174.19 -78411.2290 141177.95
## 2022.0274 42268.0908 -29566.5573 114102.74 -67593.5230 152129.70
## 2022.0301 45490.3317 -26388.1135 117368.78 -64438.2639 155418.93
## 2022.0329 56793.1483 -15129.0672 128715.36 -53202.3883 166788.68
## 2022.0356 112259.0155 40293.0561 184224.97 2196.5785 222321.45
## 2022.0384 107282.6492 35272.9727 179292.33 -2846.6474 217411.95
## 2022.0411 96352.3323 24298.9652 168405.70 -13843.7833 206548.45
## 2022.0438 85422.0155 13324.9842 157519.05 -24840.8788 195684.91
## 2022.0466 74491.6987 2351.0296 146632.37 -35837.9338 184821.33
## 2022.0493 45259.4856 -26924.7949 117443.77 -65136.8447 155655.82
## 2022.0521 8953.4189 -63274.4466 81181.28 -101509.5690 119416.41
## 2022.0548 57778.1014 -14493.3228 130049.53 -52751.5038 168307.71
## 2022.0575 37525.1881 -34789.7686 109840.14 -73070.9943 148121.37
## 2022.0603 33850.9013 -38507.5618 106209.36 -76811.8183 144513.62
## 2022.0630 56360.1118 -16041.8314 128762.06 -54369.1050 167089.33
## 2022.0658 31260.4587 -41184.9386 103705.86 -79535.2153 142056.13
## 2022.0685 62505.0205 -9983.8048 134993.85 -48357.0710 173367.11
## 2022.0712 55268.0192 -17264.2082 127800.25 -55660.4500 166196.49
## 2022.0740 96852.4872 24276.8838 169428.09 -14142.3200 207847.29
## 2022.0767 88647.1062 16028.1525 161266.06 -22413.9994 199708.21
## 2022.0795 68713.7546 -3948.5233 141376.03 -42413.6098 179841.12
## 2022.0822 48817.1677 -23888.4087 121522.74 -62376.4160 160010.75
## 2022.0849 48042.0719 -24706.7773 120790.92 -63217.6917 159301.84
## 2022.0877 2082.5295 -70709.5666 74874.63 -109243.3747 113408.43
## 2022.0904 11310.2904 -61525.0271 84145.61 -100081.7151 122702.30
## 2022.0932 12551.2690 -60327.2441 85429.78 -98906.7985 124009.34
## 2022.0959 9986.6594 -62935.0238 82908.34 -101537.4311 121510.75
## 2022.0986 5125.7285 -67839.0993 78090.56 -106464.3459 116715.80
## 2022.1014 17731.6770 -55276.2698 90739.62 -93924.3423 129387.70
## 2022.1041 43003.3429 -30047.6976 116054.38 -68718.5825 154725.27
## 2022.1068 59632.8178 -13461.2909 132726.93 -52154.9747 171420.61
## 2022.1096 59752.4648 -13384.6867 132889.62 -52101.1560 171606.09
## 2022.1123 53992.6122 -19187.5568 127172.78 -57926.7982 165912.02
## 2022.1151 31223.3374 -41999.8239 104446.50 -80761.8240 143208.50
## 2022.1178 43968.7185 -29297.4098 117234.85 -68082.1553 156019.59
## 2022.1205 62406.9117 -10902.1584 135715.98 -49709.6359 174523.46
## 2022.1233 35121.6840 -38230.3028 108473.67 -77060.4991 147303.87
## 2022.1260 65299.7387 -8095.1397 138694.62 -46948.0415 177547.52
## 2022.1288 39619.6361 -33818.1089 113057.38 -72693.7028 151932.97
## 2022.1315 70614.1412 -2866.4453 144094.73 -41764.7182 182993.00
## 2022.1342 74535.3476 1011.9445 148058.75 -37908.9941 186979.69
## 2022.1370 87597.9135 14031.7188 161164.11 -24911.8723 200107.70
## 2022.1397 75786.9932 2178.0316 149395.95 -36788.1988 188362.19
## 2022.1425 68194.7862 -5456.9173 141846.49 -44445.7740 180835.35
## 2022.1452 75916.6319 2222.2112 149611.05 -36789.2586 188622.52
## 2022.1479 81443.1471 7706.0340 155180.26 -31328.0358 194214.33
## 2022.1507 62280.7175 -11499.0632 136060.50 -50555.7200 175117.16
## 2022.1534 70169.9855 -3652.4384 143992.41 -42731.6690 183071.64
## 2022.1562 84006.2302 10141.1879 157871.27 -28960.6035 196973.06
## 2022.1589 58604.5829 -15303.0532 132512.22 -54427.3924 171636.56
## 2022.1616 94772.9079 20822.7024 168723.11 -18324.1717 207869.99
## 2022.1644 79461.4486 5468.6983 153454.20 -33700.6977 192623.59
## 2022.1671 86858.4539 12823.1833 160893.72 -26368.7216 200085.63
## 2022.1699 101868.0472 27790.2806 175945.81 -11424.1203 215160.21
## 2022.1726 59046.8608 -15073.3775 133167.10 -54310.2615 172403.98
## 2022.1753 42743.4303 -31419.2553 116906.12 -70678.6096 156165.47
## 2022.1781 11779.0055 -62426.1031 85984.11 -101707.9147 125265.93
## 2022.1808 59730.5404 -14516.9669 133978.05 -53821.2231 173282.30
## 2022.1836 62139.7769 -12150.1050 136429.66 -51476.7929 175756.35
## 2022.1863 53716.9376 -20615.2947 128049.17 -59964.4016 167398.28
## 2022.1890 40596.5939 -33777.9647 114971.15 -73149.4778 154342.67
## 2022.1918 79801.8018 5384.9410 154218.66 -34008.9656 193612.57
## 2022.1945 64000.1714 -10458.9677 138459.31 -49875.2549 177875.60
## 2022.1973 78881.3802 4379.9870 153382.77 -35058.6683 192821.43
## 2022.2000 60838.3502 -13705.2733 135381.97 -53166.2840 174842.98
## 2022.2027 66916.3404 -7669.4894 141502.17 -47152.8427 180985.52
## 2022.2055 86192.1644 11564.1521 160820.18 -27941.5313 200325.86
## 2022.2082 59001.6016 -15668.5693 133671.77 -55196.5701 173199.77
## 2022.2110 69793.5830 -4918.7228 144505.89 -44469.0284 184056.19
## 2022.2137 55061.3675 -19693.0494 129815.78 -59265.6473 169388.38
## 2022.2164 85681.3951 10884.8908 160477.90 -28709.9868 200072.78
## 2022.2192 81212.1907 6373.6227 156050.76 -33243.5222 195667.90
## 2022.2219 82866.7381 7986.1300 157747.35 -31653.2695 197386.75
## 2022.2247 80221.3467 5298.7221 155143.97 -34362.9196 194805.61
## 2022.2274 89853.6192 14889.0016 164818.24 -24794.8698 204502.11
## 2022.2301 67382.0092 -7624.5778 142388.60 -47330.6665 182094.68
## 2022.2329 67574.6584 -7473.8746 142623.19 -47202.1682 182351.48
## 2022.2356 98925.2663 23834.8108 174015.72 -15915.6753 213766.21
## 2022.2384 90096.2987 14963.9440 165228.65 -24808.7221 205001.32
## 2022.2411 108084.2601 32910.0296 183258.49 -6884.8042 223053.32
## 2022.2438 104931.9710 29715.8880 180148.05 -10101.1012 219965.04
## 2022.2466 103934.8315 28676.9193 179192.74 -11162.2129 219031.88
## 2022.2493 72011.2374 -3288.4808 147310.96 -43149.7437 187172.22
## 2022.2521 41767.7903 -33573.7106 117109.29 -73457.0920 156992.67
## 2022.2548 47945.5437 -27437.7169 123328.80 -67343.2045 163234.29
## 2022.2575 99133.3281 23708.3311 174558.33 -16219.2505 214485.91
## 2022.2603 82492.6739 7025.9634 157959.38 -32923.6999 197909.05
## 2022.2630 85422.3875 9913.9867 160930.79 -30057.7462 200902.52
## 2022.2658 69615.7374 -5934.3308 145165.81 -45928.1211 185159.60
## 2022.2685 80901.3151 5309.6025 156493.03 -34706.2330 196508.86
## 2022.2712 104352.4880 28719.1539 179985.82 -11318.7146 220023.69
## 2022.2740 77375.5133 1700.5806 153050.45 -38359.3089 193110.34
## 2022.2767 44332.7225 -31383.7859 120049.23 -71465.6842 160131.13
## 2022.2795 56915.7854 -18842.2759 132673.85 -58946.1710 172777.74
## 2022.2822 96209.4520 20409.8606 172009.04 -19716.0193 212134.92
## 2022.2849 94315.6332 18474.5344 170156.73 -21673.3181 210304.58
## 2022.2877 61738.3847 -14144.1988 137620.97 -54314.0120 177790.78
## 2022.2904 66172.7359 -9751.3096 142096.78 -49943.0715 182288.54
## 2022.2932 107975.9088 32010.4239 183941.39 -8203.2747 224155.09
## 2022.2959 86422.5691 10415.6674 162429.47 -29819.9558 202665.09
## 2022.2986 96569.8391 20521.5432 172618.13 -19735.9929 212875.67
## 2022.3014 114584.3428 38494.6752 190674.01 -1784.7618 230953.45
## 2022.3041 110518.8472 34387.8303 186649.86 -5913.4956 226951.19
## 2022.3068 94408.6802 18236.3366 170581.02 -22086.8664 210904.23
## 2022.3096 79810.9652 3597.3172 156024.61 -36747.7509 196369.68
## 2022.3123 60800.6190 -15454.3110 137055.55 -55821.2325 177422.47
## 2022.3151 56936.9461 -19359.2435 133233.14 -59748.0066 173621.90
## 2022.3178 75902.6371 -434.7899 152240.06 -40845.3828 192650.66
## 2022.3205 53924.8288 -22453.8133 130303.47 -62886.2241 170735.88
## 2022.3233 28281.3034 -48138.5316 104701.14 -88592.7486 145155.36
## 2022.3260 39401.5199 -37059.4858 115862.53 -77535.4972 156338.54
## 2022.3288 78269.7967 1767.6425 154771.95 -38730.1517 195269.75
## 2022.3315 102202.1994 25658.9188 178745.48 -14860.6464 219265.05
## 2022.3342 112243.4113 35659.0264 188827.80 -4882.2981 229369.12
## 2022.3370 103021.2765 26395.8093 179646.74 -14167.2628 220209.82
## 2022.3397 79422.5818 2756.0544 156089.11 -37828.7537 196673.92
## 2022.3425 64362.9686 -12344.5971 141070.53 -52951.1296 181677.07
## 2022.3452 67857.0911 -8891.4909 144605.67 -49519.7361 185233.92
## 2022.3479 49865.4822 -26924.0943 126655.06 -67574.0406 167305.00
## 2022.3507 64502.4187 -12328.1303 141332.97 -52999.7662 182004.60
## 2022.3534 109423.7798 32552.2800 186295.28 -8141.0338 226988.59
## 2022.3562 114988.7673 38076.3387 191901.20 -2638.6417 232616.18
## 2022.3589 120689.4693 43736.1335 197642.81 2999.4982 238379.44
## 2022.3616 84164.7645 7170.5433 161158.99 -33587.7354 201917.26
## 2022.3644 59261.5608 -17773.5241 136296.65 -58553.4348 177076.56
## 2022.3671 23713.8265 -53362.1005 100789.75 -94163.6316 141591.28
## 2022.3699 62469.4536 -14647.2938 139586.20 -55470.4339 180409.34
## 2022.3726 89481.9981 12324.4519 166639.54 -28520.2858 207484.28
## 2022.3753 74822.8096 -2375.5139 152021.13 -43241.8377 192887.46
## 2022.3781 56428.4678 -20810.6113 133667.55 -61698.5100 174555.45
## 2022.3808 112944.2080 35664.3946 190224.02 -5245.0675 231133.48
## 2022.3836 121641.8678 44321.3416 198962.39 3390.3275 239893.41
## 2022.3863 105277.1198 27915.9022 182638.34 -13036.6526 223590.89
## 2022.3890 105531.8358 28129.9483 182933.72 -12844.1359 223907.81
## 2022.3918 82200.7307 4758.1946 159643.27 -36237.4076 200638.87
## 2022.3945 71058.6000 -6424.5633 148541.76 -47441.6723 189558.87
## 2022.3973 58370.0468 -19153.7225 135893.82 -60192.3270 176932.42
## 2022.4000 82669.1685 5104.8145 160233.52 -35955.2743 201293.61
## 2022.4027 79047.7052 1442.7877 156652.62 -39638.7741 197734.18
## 2022.4055 90190.5623 12545.1025 167836.02 -28557.9211 208939.05
## 2022.4082 74833.3011 -2852.6799 152519.28 -43977.1541 193643.76
## 2022.4110 64236.6242 -13489.8568 141963.11 -54635.7705 183109.02
## 2022.4137 47357.4291 -30409.5309 125124.39 -71576.8727 166291.73
## 2022.4164 34687.0353 -43120.3825 112494.45 -84309.1415 153683.21
## 2022.4192 18993.7757 -58854.0789 96841.63 -100064.2439 138051.80
## 2022.4219 30017.0406 -47871.2299 107905.31 -89102.7897 149136.87
## 2022.4247 51039.8882 -26888.7772 128968.55 -68141.7207 170221.50
## 2022.4274 73275.0192 -4694.0202 151244.06 -45968.3365 192518.37
## 2022.4301 76760.2535 -1249.1390 154769.65 -42544.8169 196065.32
## 2022.4329 75586.3048 -2463.4199 153636.03 -43780.4484 194953.06
## 2022.4356 73160.0867 -4929.9494 151250.12 -46268.3174 192588.49
## 2022.4384 51927.4592 -26202.8674 130057.79 -67562.5640 171417.48
## 2022.4411 54988.4727 -23182.1237 133159.07 -64563.1378 174540.08
## 2022.4438 81228.4608 3017.6153 159439.31 -38384.7054 200841.63
## 2022.4466 84948.4289 6697.3550 163199.50 -34726.2613 204623.12
## 2022.4493 93214.7386 14923.4570 171506.02 -26521.4440 212950.92
## 2022.4521 84892.8457 6561.3770 163224.31 -34904.7977 204690.49
## 2022.4548 102813.0100 24441.3749 181184.65 -17046.0626 222672.08
## 2022.4575 51519.3555 -26892.4254 129931.14 -68401.1149 171439.83
## 2022.4603 55903.8275 -22548.0788 134355.73 -64078.0094 175885.66
## 2022.4630 66783.9704 -11708.0408 145275.98 -53259.2015 186827.14
## 2022.4658 49247.3183 -29284.7772 127779.41 -70857.1573 169351.79
## 2022.4685 51382.0940 -27190.0654 129954.25 -68783.6541 171547.84
## 2022.4712 79125.2720 513.0691 157737.47 -41101.7173 199352.26
## 2022.4740 69664.2673 -8987.9587 148316.49 -50623.9320 189952.47
## 2022.4767 82218.9795 3526.7509 160911.21 -38130.3987 202568.36
## 2022.4795 87666.5995 8934.3884 166398.81 -32743.9265 208077.13
## 2022.4822 97080.5068 18308.3336 175852.68 -23391.1360 217552.15
## 2022.4849 96803.8612 17991.7462 175615.98 -23728.8674 217336.59
## 2022.4877 101924.3145 23072.2779 180776.35 -18669.4689 222518.10
## 2022.4904 90913.6458 12021.7077 169805.58 -29741.1616 211568.45##create forecast and actual data line together, create overlap plot
#red line deviates from the black peaks and bottoms
ts.plot(turbine_tsi, fitted(fit_AR3), gpars=list(col=c("black","red")))
#fit the original line well, pretty goodCreate matrix of covariates for next 5 time periods
xdat <- c(5.73, 4.03, 3.88, 5.01, 4.51)
xdat1 <- matrix(xdat, nrow = 5, ncol = 1, byrow = TRUE)
xregmat = day_turbine1$wind_speed##Re-run model with ARIMA and produce forcast for next 5 days
fit_AR3_v2 <- Arima(turbine_tsi, xreg = xregmat, order = c(2,1,1))
forecast(fit_AR3_v2, xreg = xdat1, h = 5)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2020.2466 95691.92 75056.868 116326.97 64133.332 127250.51
## 2020.2493 45254.71 17471.239 73038.17 2763.559 87745.85
## 2020.2521 38432.54 7658.566 69206.51 -8632.190 85497.26
## 2020.2548 67648.10 35599.034 99697.17 18633.283 116662.92
## 2020.2575 53040.16 20398.333 85681.98 3118.796 102961.51autoplot(forecast(fit_AR3_v2, xreg = xdat1, h = 5))